Actual source code: fieldsplit.c
1: #include <petsc/private/pcimpl.h>
2: #include <petsc/private/kspimpl.h>
3: #include <petscdm.h>
5: const char *const PCFieldSplitSchurPreTypes[] = {"SELF", "SELFP", "A11", "USER", "FULL", "PCFieldSplitSchurPreType", "PC_FIELDSPLIT_SCHUR_PRE_", NULL};
6: const char *const PCFieldSplitSchurFactTypes[] = {"DIAG", "LOWER", "UPPER", "FULL", "PCFieldSplitSchurFactType", "PC_FIELDSPLIT_SCHUR_FACT_", NULL};
8: PetscLogEvent KSP_Solve_FS_0, KSP_Solve_FS_1, KSP_Solve_FS_S, KSP_Solve_FS_U, KSP_Solve_FS_L, KSP_Solve_FS_2, KSP_Solve_FS_3, KSP_Solve_FS_4;
10: typedef struct _PC_FieldSplitLink *PC_FieldSplitLink;
11: struct _PC_FieldSplitLink {
12: KSP ksp;
13: Vec x, y, z;
14: char *splitname;
15: PetscInt nfields;
16: PetscInt *fields, *fields_col;
17: VecScatter sctx;
18: IS is, is_col;
19: PC_FieldSplitLink next, previous;
20: PetscLogEvent event;
22: /* Used only when setting coordinates with PCSetCoordinates */
23: PetscInt dim;
24: PetscInt ndofs;
25: PetscReal *coords;
26: };
28: typedef struct {
29: PCCompositeType type;
30: PetscBool defaultsplit; /* Flag for a system with a set of 'k' scalar fields with the same layout (and bs = k) */
31: PetscBool splitdefined; /* Flag is set after the splits have been defined, to prevent more splits from being added */
32: PetscInt bs; /* Block size for IS and Mat structures */
33: PetscInt nsplits; /* Number of field divisions defined */
34: Vec *x, *y, w1, w2;
35: Mat *mat; /* The diagonal block for each split */
36: Mat *pmat; /* The preconditioning diagonal block for each split */
37: Mat *Afield; /* The rows of the matrix associated with each split */
38: PetscBool issetup;
40: /* Only used when Schur complement preconditioning is used */
41: Mat B; /* The (0,1) block */
42: Mat C; /* The (1,0) block */
43: Mat schur; /* The Schur complement S = A11 - A10 A00^{-1} A01, the KSP here, kspinner, is H_1 in [El08] */
44: Mat schurp; /* Assembled approximation to S built by MatSchurComplement to be used as a preconditioning matrix when solving with S */
45: Mat schur_user; /* User-provided preconditioning matrix for the Schur complement */
46: PCFieldSplitSchurPreType schurpre; /* Determines which preconditioning matrix is used for the Schur complement */
47: PCFieldSplitSchurFactType schurfactorization;
48: KSP kspschur; /* The solver for S */
49: KSP kspupper; /* The solver for A in the upper diagonal part of the factorization (H_2 in [El08]) */
50: PetscScalar schurscale; /* Scaling factor for the Schur complement solution with DIAG factorization */
52: /* Only used when Golub-Kahan bidiagonalization preconditioning is used */
53: Mat H; /* The modified matrix H = A00 + nu*A01*A01' */
54: PetscReal gkbtol; /* Stopping tolerance for lower bound estimate */
55: PetscInt gkbdelay; /* The delay window for the stopping criterion */
56: PetscReal gkbnu; /* Parameter for augmented Lagrangian H = A + nu*A01*A01' */
57: PetscInt gkbmaxit; /* Maximum number of iterations for outer loop */
58: PetscBool gkbmonitor; /* Monitor for gkb iterations and the lower bound error */
59: PetscViewer gkbviewer; /* Viewer context for gkbmonitor */
60: Vec u, v, d, Hu; /* Work vectors for the GKB algorithm */
61: PetscScalar *vecz; /* Contains intermediate values, eg for lower bound */
63: PC_FieldSplitLink head;
64: PetscBool isrestrict; /* indicates PCFieldSplitRestrictIS() has been last called on this object, hack */
65: PetscBool suboptionsset; /* Indicates that the KSPSetFromOptions() has been called on the sub-KSPs */
66: PetscBool dm_splits; /* Whether to use DMCreateFieldDecomposition() whenever possible */
67: PetscBool diag_use_amat; /* Whether to extract diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */
68: PetscBool offdiag_use_amat; /* Whether to extract off-diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */
69: PetscBool detect; /* Whether to form 2-way split by finding zero diagonal entries */
70: PetscBool coordinates_set; /* Whether PCSetCoordinates has been called */
71: } PC_FieldSplit;
73: /*
74: Note:
75: there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of
76: inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the
77: PC you could change this.
78: */
80: /* This helper is so that setting a user-provided preconditioning matrix is orthogonal to choosing to use it. This way the
81: * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */
82: static Mat FieldSplitSchurPre(PC_FieldSplit *jac)
83: {
84: switch (jac->schurpre) {
85: case PC_FIELDSPLIT_SCHUR_PRE_SELF:
86: return jac->schur;
87: case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
88: return jac->schurp;
89: case PC_FIELDSPLIT_SCHUR_PRE_A11:
90: return jac->pmat[1];
91: case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */
92: case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */
93: default:
94: return jac->schur_user ? jac->schur_user : jac->pmat[1];
95: }
96: }
98: #include <petscdraw.h>
99: static PetscErrorCode PCView_FieldSplit(PC pc, PetscViewer viewer)
100: {
101: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
102: PetscBool iascii, isdraw;
103: PetscInt i, j;
104: PC_FieldSplitLink ilink = jac->head;
106: PetscFunctionBegin;
107: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
108: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
109: if (iascii) {
110: if (jac->bs > 0) {
111: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs));
112: } else {
113: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits));
114: }
115: if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n"));
116: if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for diagonal blocks\n"));
117: if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for off-diagonal blocks\n"));
118: PetscCall(PetscViewerASCIIPrintf(viewer, " Solver info for each split is in the following KSP objects:\n"));
119: for (i = 0; i < jac->nsplits; i++) {
120: if (ilink->fields) {
121: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i));
122: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
123: for (j = 0; j < ilink->nfields; j++) {
124: if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
125: PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
126: }
127: PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
128: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
129: } else {
130: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i));
131: }
132: PetscCall(KSPView(ilink->ksp, viewer));
133: ilink = ilink->next;
134: }
135: }
137: if (isdraw) {
138: PetscDraw draw;
139: PetscReal x, y, w, wd;
141: PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
142: PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
143: w = 2 * PetscMin(1.0 - x, x);
144: wd = w / (jac->nsplits + 1);
145: x = x - wd * (jac->nsplits - 1) / 2.0;
146: for (i = 0; i < jac->nsplits; i++) {
147: PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
148: PetscCall(KSPView(ilink->ksp, viewer));
149: PetscCall(PetscDrawPopCurrentPoint(draw));
150: x += wd;
151: ilink = ilink->next;
152: }
153: }
154: PetscFunctionReturn(PETSC_SUCCESS);
155: }
157: static PetscErrorCode PCView_FieldSplit_Schur(PC pc, PetscViewer viewer)
158: {
159: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
160: PetscBool iascii, isdraw;
161: PetscInt i, j;
162: PC_FieldSplitLink ilink = jac->head;
163: MatSchurComplementAinvType atype;
165: PetscFunctionBegin;
166: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
167: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
168: if (iascii) {
169: if (jac->bs > 0) {
170: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with Schur preconditioner, blocksize = %" PetscInt_FMT ", factorization %s\n", jac->bs, PCFieldSplitSchurFactTypes[jac->schurfactorization]));
171: } else {
172: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with Schur preconditioner, factorization %s\n", PCFieldSplitSchurFactTypes[jac->schurfactorization]));
173: }
174: if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n"));
175: switch (jac->schurpre) {
176: case PC_FIELDSPLIT_SCHUR_PRE_SELF:
177: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from S itself\n"));
178: break;
179: case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
180: if (jac->schur) {
181: PetscCall(MatSchurComplementGetAinvType(jac->schur, &atype));
182: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's %sinverse\n", atype == MAT_SCHUR_COMPLEMENT_AINV_DIAG ? "diagonal's " : (atype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG ? "block diagonal's " : (atype == MAT_SCHUR_COMPLEMENT_AINV_FULL ? "full " : "lumped diagonal's "))));
183: }
184: break;
185: case PC_FIELDSPLIT_SCHUR_PRE_A11:
186: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from A11\n"));
187: break;
188: case PC_FIELDSPLIT_SCHUR_PRE_FULL:
189: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from the exact Schur complement\n"));
190: break;
191: case PC_FIELDSPLIT_SCHUR_PRE_USER:
192: if (jac->schur_user) {
193: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from user provided matrix\n"));
194: } else {
195: PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from A11\n"));
196: }
197: break;
198: default:
199: SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Invalid Schur preconditioning type: %d", jac->schurpre);
200: }
201: PetscCall(PetscViewerASCIIPrintf(viewer, " Split info:\n"));
202: PetscCall(PetscViewerASCIIPushTab(viewer));
203: for (i = 0; i < jac->nsplits; i++) {
204: if (ilink->fields) {
205: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i));
206: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
207: for (j = 0; j < ilink->nfields; j++) {
208: if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
209: PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
210: }
211: PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
212: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
213: } else {
214: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i));
215: }
216: ilink = ilink->next;
217: }
218: PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for A00 block\n"));
219: PetscCall(PetscViewerASCIIPushTab(viewer));
220: if (jac->head) {
221: PetscCall(KSPView(jac->head->ksp, viewer));
222: } else PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n"));
223: PetscCall(PetscViewerASCIIPopTab(viewer));
224: if (jac->head && jac->kspupper != jac->head->ksp) {
225: PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for upper A00 in upper triangular factor\n"));
226: PetscCall(PetscViewerASCIIPushTab(viewer));
227: if (jac->kspupper) PetscCall(KSPView(jac->kspupper, viewer));
228: else PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n"));
229: PetscCall(PetscViewerASCIIPopTab(viewer));
230: }
231: PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for S = A11 - A10 inv(A00) A01\n"));
232: PetscCall(PetscViewerASCIIPushTab(viewer));
233: if (jac->kspschur) {
234: PetscCall(KSPView(jac->kspschur, viewer));
235: } else {
236: PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n"));
237: }
238: PetscCall(PetscViewerASCIIPopTab(viewer));
239: PetscCall(PetscViewerASCIIPopTab(viewer));
240: } else if (isdraw && jac->head) {
241: PetscDraw draw;
242: PetscReal x, y, w, wd, h;
243: PetscInt cnt = 2;
244: char str[32];
246: PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
247: PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
248: if (jac->kspupper != jac->head->ksp) cnt++;
249: w = 2 * PetscMin(1.0 - x, x);
250: wd = w / (cnt + 1);
252: PetscCall(PetscSNPrintf(str, 32, "Schur fact. %s", PCFieldSplitSchurFactTypes[jac->schurfactorization]));
253: PetscCall(PetscDrawStringBoxed(draw, x, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h));
254: y -= h;
255: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_USER && !jac->schur_user) {
256: PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[PC_FIELDSPLIT_SCHUR_PRE_A11]));
257: } else {
258: PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[jac->schurpre]));
259: }
260: PetscCall(PetscDrawStringBoxed(draw, x + wd * (cnt - 1) / 2.0, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h));
261: y -= h;
262: x = x - wd * (cnt - 1) / 2.0;
264: PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
265: PetscCall(KSPView(jac->head->ksp, viewer));
266: PetscCall(PetscDrawPopCurrentPoint(draw));
267: if (jac->kspupper != jac->head->ksp) {
268: x += wd;
269: PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
270: PetscCall(KSPView(jac->kspupper, viewer));
271: PetscCall(PetscDrawPopCurrentPoint(draw));
272: }
273: x += wd;
274: PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
275: PetscCall(KSPView(jac->kspschur, viewer));
276: PetscCall(PetscDrawPopCurrentPoint(draw));
277: }
278: PetscFunctionReturn(PETSC_SUCCESS);
279: }
281: static PetscErrorCode PCView_FieldSplit_GKB(PC pc, PetscViewer viewer)
282: {
283: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
284: PetscBool iascii, isdraw;
285: PetscInt i, j;
286: PC_FieldSplitLink ilink = jac->head;
288: PetscFunctionBegin;
289: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
290: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
291: if (iascii) {
292: if (jac->bs > 0) {
293: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs));
294: } else {
295: PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits));
296: }
297: if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n"));
298: if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for diagonal blocks\n"));
299: if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for off-diagonal blocks\n"));
301: PetscCall(PetscViewerASCIIPrintf(viewer, " Stopping tolerance=%.1e, delay in error estimate=%" PetscInt_FMT ", maximum iterations=%" PetscInt_FMT "\n", (double)jac->gkbtol, jac->gkbdelay, jac->gkbmaxit));
302: PetscCall(PetscViewerASCIIPrintf(viewer, " Solver info for H = A00 + nu*A01*A01' matrix:\n"));
303: PetscCall(PetscViewerASCIIPushTab(viewer));
305: if (ilink->fields) {
306: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Fields "));
307: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
308: for (j = 0; j < ilink->nfields; j++) {
309: if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
310: PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
311: }
312: PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
313: PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
314: } else {
315: PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Defined by IS\n"));
316: }
317: PetscCall(KSPView(ilink->ksp, viewer));
319: PetscCall(PetscViewerASCIIPopTab(viewer));
320: }
322: if (isdraw) {
323: PetscDraw draw;
324: PetscReal x, y, w, wd;
326: PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
327: PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
328: w = 2 * PetscMin(1.0 - x, x);
329: wd = w / (jac->nsplits + 1);
330: x = x - wd * (jac->nsplits - 1) / 2.0;
331: for (i = 0; i < jac->nsplits; i++) {
332: PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
333: PetscCall(KSPView(ilink->ksp, viewer));
334: PetscCall(PetscDrawPopCurrentPoint(draw));
335: x += wd;
336: ilink = ilink->next;
337: }
338: }
339: PetscFunctionReturn(PETSC_SUCCESS);
340: }
342: /* Precondition: jac->bs is set to a meaningful value */
343: static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc)
344: {
345: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
346: PetscInt i, nfields, *ifields, nfields_col, *ifields_col;
347: PetscBool flg, flg_col;
348: char optionname[128], splitname[8], optionname_col[128];
350: PetscFunctionBegin;
351: PetscCall(PetscMalloc1(jac->bs, &ifields));
352: PetscCall(PetscMalloc1(jac->bs, &ifields_col));
353: for (i = 0, flg = PETSC_TRUE;; i++) {
354: PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
355: PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
356: PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i));
357: nfields = jac->bs;
358: nfields_col = jac->bs;
359: PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
360: PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col));
361: if (!flg) break;
362: else if (flg && !flg_col) {
363: PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
364: PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields));
365: } else {
366: PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
367: PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match");
368: PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col));
369: }
370: }
371: if (i > 0) {
372: /* Makes command-line setting of splits take precedence over setting them in code.
373: Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
374: create new splits, which would probably not be what the user wanted. */
375: jac->splitdefined = PETSC_TRUE;
376: }
377: PetscCall(PetscFree(ifields));
378: PetscCall(PetscFree(ifields_col));
379: PetscFunctionReturn(PETSC_SUCCESS);
380: }
382: static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
383: {
384: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
385: PC_FieldSplitLink ilink = jac->head;
386: PetscBool fieldsplit_default = PETSC_FALSE, coupling = PETSC_FALSE;
387: PetscInt i;
389: PetscFunctionBegin;
390: /*
391: Kinda messy, but at least this now uses DMCreateFieldDecomposition().
392: Should probably be rewritten.
393: */
394: if (!ilink) {
395: PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_detect_coupling", &coupling, NULL));
396: if (pc->dm && jac->dm_splits && !jac->detect && !coupling) {
397: PetscInt numFields, f, i, j;
398: char **fieldNames;
399: IS *fields;
400: DM *dms;
401: DM subdm[128];
402: PetscBool flg;
404: PetscCall(DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms));
405: /* Allow the user to prescribe the splits */
406: for (i = 0, flg = PETSC_TRUE;; i++) {
407: PetscInt ifields[128];
408: IS compField;
409: char optionname[128], splitname[8];
410: PetscInt nfields = numFields;
412: PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
413: PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
414: if (!flg) break;
415: PetscCheck(numFields <= 128, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot currently support %" PetscInt_FMT " > 128 fields", numFields);
416: PetscCall(DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i]));
417: if (nfields == 1) {
418: PetscCall(PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField));
419: } else {
420: PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
421: PetscCall(PCFieldSplitSetIS(pc, splitname, compField));
422: }
423: PetscCall(ISDestroy(&compField));
424: for (j = 0; j < nfields; ++j) {
425: f = ifields[j];
426: PetscCall(PetscFree(fieldNames[f]));
427: PetscCall(ISDestroy(&fields[f]));
428: }
429: }
430: if (i == 0) {
431: for (f = 0; f < numFields; ++f) {
432: PetscCall(PCFieldSplitSetIS(pc, fieldNames[f], fields[f]));
433: PetscCall(PetscFree(fieldNames[f]));
434: PetscCall(ISDestroy(&fields[f]));
435: }
436: } else {
437: for (j = 0; j < numFields; j++) PetscCall(DMDestroy(dms + j));
438: PetscCall(PetscFree(dms));
439: PetscCall(PetscMalloc1(i, &dms));
440: for (j = 0; j < i; ++j) dms[j] = subdm[j];
441: }
442: PetscCall(PetscFree(fieldNames));
443: PetscCall(PetscFree(fields));
444: if (dms) {
445: PetscCall(PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n"));
446: for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) {
447: const char *prefix;
448: PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ilink->ksp, &prefix));
449: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dms[i], prefix));
450: PetscCall(KSPSetDM(ilink->ksp, dms[i]));
451: PetscCall(KSPSetDMActive(ilink->ksp, PETSC_FALSE));
452: {
453: PetscErrorCode (*func)(KSP, Mat, Mat, void *);
454: void *ctx;
456: PetscCall(DMKSPGetComputeOperators(pc->dm, &func, &ctx));
457: PetscCall(DMKSPSetComputeOperators(dms[i], func, ctx));
458: }
459: PetscCall(PetscObjectIncrementTabLevel((PetscObject)dms[i], (PetscObject)ilink->ksp, 0));
460: PetscCall(DMDestroy(&dms[i]));
461: }
462: PetscCall(PetscFree(dms));
463: }
464: } else {
465: if (jac->bs <= 0) {
466: if (pc->pmat) {
467: PetscCall(MatGetBlockSize(pc->pmat, &jac->bs));
468: } else jac->bs = 1;
469: }
471: if (jac->detect) {
472: IS zerodiags, rest;
473: PetscInt nmin, nmax;
475: PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
476: if (jac->diag_use_amat) {
477: PetscCall(MatFindZeroDiagonals(pc->mat, &zerodiags));
478: } else {
479: PetscCall(MatFindZeroDiagonals(pc->pmat, &zerodiags));
480: }
481: PetscCall(ISComplement(zerodiags, nmin, nmax, &rest));
482: PetscCall(PCFieldSplitSetIS(pc, "0", rest));
483: PetscCall(PCFieldSplitSetIS(pc, "1", zerodiags));
484: PetscCall(ISDestroy(&zerodiags));
485: PetscCall(ISDestroy(&rest));
486: } else if (coupling) {
487: IS coupling, rest;
488: PetscInt nmin, nmax;
490: PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
491: if (jac->offdiag_use_amat) {
492: PetscCall(MatFindOffBlockDiagonalEntries(pc->mat, &coupling));
493: } else {
494: PetscCall(MatFindOffBlockDiagonalEntries(pc->pmat, &coupling));
495: }
496: PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc->mat), nmax - nmin, nmin, 1, &rest));
497: PetscCall(ISSetIdentity(rest));
498: PetscCall(PCFieldSplitSetIS(pc, "0", rest));
499: PetscCall(PCFieldSplitSetIS(pc, "1", coupling));
500: PetscCall(ISDestroy(&coupling));
501: PetscCall(ISDestroy(&rest));
502: } else {
503: PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_default", &fieldsplit_default, NULL));
504: if (!fieldsplit_default) {
505: /* Allow user to set fields from command line, if bs was known at the time of PCSetFromOptions_FieldSplit()
506: then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
507: PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
508: if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
509: }
510: if ((fieldsplit_default || !jac->splitdefined) && !jac->isrestrict) {
511: Mat M = pc->pmat;
512: PetscBool isnest;
514: PetscCall(PetscInfo(pc, "Using default splitting of fields\n"));
515: PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &isnest));
516: if (!isnest) {
517: M = pc->mat;
518: PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &isnest));
519: }
520: if (isnest) {
521: IS *fields;
522: PetscInt nf;
524: PetscCall(MatNestGetSize(M, &nf, NULL));
525: PetscCall(PetscMalloc1(nf, &fields));
526: PetscCall(MatNestGetISs(M, fields, NULL));
527: for (i = 0; i < nf; i++) PetscCall(PCFieldSplitSetIS(pc, NULL, fields[i]));
528: PetscCall(PetscFree(fields));
529: } else {
530: for (i = 0; i < jac->bs; i++) {
531: char splitname[8];
532: PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
533: PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i));
534: }
535: jac->defaultsplit = PETSC_TRUE;
536: }
537: }
538: }
539: }
540: } else if (jac->nsplits == 1) {
541: IS is2;
542: PetscInt nmin, nmax;
544: PetscCheck(ilink->is, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Must provide at least two sets of fields to PCFieldSplit()");
545: PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
546: PetscCall(ISComplement(ilink->is, nmin, nmax, &is2));
547: PetscCall(PCFieldSplitSetIS(pc, "1", is2));
548: PetscCall(ISDestroy(&is2));
549: }
551: PetscCheck(jac->nsplits >= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unhandled case, must have at least two fields, not %" PetscInt_FMT, jac->nsplits);
552: PetscFunctionReturn(PETSC_SUCCESS);
553: }
555: static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu)
556: {
557: Mat BT, T;
558: PetscReal nrmT, nrmB;
560: PetscFunctionBegin;
561: PetscCall(MatHermitianTranspose(C, MAT_INITIAL_MATRIX, &T)); /* Test if augmented matrix is symmetric */
562: PetscCall(MatAXPY(T, -1.0, B, DIFFERENT_NONZERO_PATTERN));
563: PetscCall(MatNorm(T, NORM_1, &nrmT));
564: PetscCall(MatNorm(B, NORM_1, &nrmB));
565: PetscCheck(nrmB <= 0 || nrmT / nrmB < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix is not symmetric/hermitian, GKB is not applicable.");
567: /* Compute augmented Lagrangian matrix H = A00 + nu*A01*A01'. This corresponds to */
568: /* setting N := 1/nu*I in [Ar13]. */
569: PetscCall(MatHermitianTranspose(B, MAT_INITIAL_MATRIX, &BT));
570: PetscCall(MatMatMult(B, BT, MAT_INITIAL_MATRIX, PETSC_DEFAULT, H)); /* H = A01*A01' */
571: PetscCall(MatAYPX(*H, gkbnu, A, DIFFERENT_NONZERO_PATTERN)); /* H = A00 + nu*A01*A01' */
573: PetscCall(MatDestroy(&BT));
574: PetscCall(MatDestroy(&T));
575: PetscFunctionReturn(PETSC_SUCCESS);
576: }
578: PETSC_EXTERN PetscErrorCode PetscOptionsFindPairPrefix_Private(PetscOptions, const char pre[], const char name[], const char *option[], const char *value[], PetscBool *flg);
580: static PetscErrorCode PCSetUp_FieldSplit(PC pc)
581: {
582: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
583: PC_FieldSplitLink ilink;
584: PetscInt i, nsplit;
585: PetscBool sorted, sorted_col;
587: PetscFunctionBegin;
588: pc->failedreason = PC_NOERROR;
589: PetscCall(PCFieldSplitSetDefaults(pc));
590: nsplit = jac->nsplits;
591: ilink = jac->head;
593: /* get the matrices for each split */
594: if (!jac->issetup) {
595: PetscInt rstart, rend, nslots, bs;
597: jac->issetup = PETSC_TRUE;
599: /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
600: if (jac->defaultsplit || !ilink->is) {
601: if (jac->bs <= 0) jac->bs = nsplit;
602: }
604: /* MatCreateSubMatrix() for [S]BAIJ matrices can only work if the indices include entire blocks of the matrix */
605: PetscCall(MatGetBlockSize(pc->pmat, &bs));
606: if (bs > 1 && (jac->bs <= bs || jac->bs % bs)) {
607: PetscBool blk;
609: PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
610: PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
611: }
613: bs = jac->bs;
614: PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
615: nslots = (rend - rstart) / bs;
616: for (i = 0; i < nsplit; i++) {
617: if (jac->defaultsplit) {
618: PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is));
619: PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
620: } else if (!ilink->is) {
621: if (ilink->nfields > 1) {
622: PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col;
623: PetscCall(PetscMalloc1(ilink->nfields * nslots, &ii));
624: PetscCall(PetscMalloc1(ilink->nfields * nslots, &jj));
625: for (j = 0; j < nslots; j++) {
626: for (k = 0; k < nfields; k++) {
627: ii[nfields * j + k] = rstart + bs * j + fields[k];
628: jj[nfields * j + k] = rstart + bs * j + fields_col[k];
629: }
630: }
631: PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, ii, PETSC_OWN_POINTER, &ilink->is));
632: PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, jj, PETSC_OWN_POINTER, &ilink->is_col));
633: PetscCall(ISSetBlockSize(ilink->is, nfields));
634: PetscCall(ISSetBlockSize(ilink->is_col, nfields));
635: } else {
636: PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields[0], bs, &ilink->is));
637: PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields_col[0], bs, &ilink->is_col));
638: }
639: }
640: PetscCall(ISSorted(ilink->is, &sorted));
641: if (ilink->is_col) PetscCall(ISSorted(ilink->is_col, &sorted_col));
642: PetscCheck(sorted && sorted_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Fields must be sorted when creating split");
643: ilink = ilink->next;
644: }
645: }
647: ilink = jac->head;
648: if (!jac->pmat) {
649: Vec xtmp;
651: PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
652: PetscCall(PetscMalloc1(nsplit, &jac->pmat));
653: PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
654: for (i = 0; i < nsplit; i++) {
655: MatNullSpace sp;
657: /* Check for preconditioning matrix attached to IS */
658: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i]));
659: if (jac->pmat[i]) {
660: PetscCall(PetscObjectReference((PetscObject)jac->pmat[i]));
661: if (jac->type == PC_COMPOSITE_SCHUR) {
662: jac->schur_user = jac->pmat[i];
664: PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
665: }
666: } else {
667: const char *prefix;
668: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
669: PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
670: if (!prefix) {
671: PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
672: PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
673: }
674: PetscCall(MatSetFromOptions(jac->pmat[i]));
675: PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
676: }
677: /* create work vectors for each split */
678: PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
679: ilink->x = jac->x[i];
680: ilink->y = jac->y[i];
681: ilink->z = NULL;
682: /* compute scatter contexts needed by multiplicative versions and non-default splits */
683: PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
684: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
685: if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
686: ilink = ilink->next;
687: }
688: PetscCall(VecDestroy(&xtmp));
689: } else {
690: MatReuse scall;
691: MatNullSpace *nullsp = NULL;
693: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
694: PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
695: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
696: scall = MAT_INITIAL_MATRIX;
697: } else scall = MAT_REUSE_MATRIX;
699: for (i = 0; i < nsplit; i++) {
700: Mat pmat;
702: /* Check for preconditioning matrix attached to IS */
703: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
704: if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
705: ilink = ilink->next;
706: }
707: if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
708: }
709: if (jac->diag_use_amat) {
710: ilink = jac->head;
711: if (!jac->mat) {
712: PetscCall(PetscMalloc1(nsplit, &jac->mat));
713: for (i = 0; i < nsplit; i++) {
714: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
715: ilink = ilink->next;
716: }
717: } else {
718: MatReuse scall;
719: MatNullSpace *nullsp = NULL;
721: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
722: PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp));
723: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
724: scall = MAT_INITIAL_MATRIX;
725: } else scall = MAT_REUSE_MATRIX;
727: for (i = 0; i < nsplit; i++) {
728: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
729: ilink = ilink->next;
730: }
731: if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
732: }
733: } else {
734: jac->mat = jac->pmat;
735: }
737: /* Check for null space attached to IS */
738: ilink = jac->head;
739: for (i = 0; i < nsplit; i++) {
740: MatNullSpace sp;
742: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
743: if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
744: ilink = ilink->next;
745: }
747: if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
748: /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
749: /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
750: ilink = jac->head;
751: if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
752: /* special case need where Afield[0] is not needed and only certain columns of Afield[1] are needed since update is only on those rows of the solution */
753: if (!jac->Afield) {
754: PetscCall(PetscCalloc1(nsplit, &jac->Afield));
755: if (jac->offdiag_use_amat) {
756: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
757: } else {
758: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
759: }
760: } else {
761: MatReuse scall;
763: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
764: PetscCall(MatDestroy(&jac->Afield[1]));
765: scall = MAT_INITIAL_MATRIX;
766: } else scall = MAT_REUSE_MATRIX;
768: if (jac->offdiag_use_amat) {
769: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
770: } else {
771: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
772: }
773: }
774: } else {
775: if (!jac->Afield) {
776: PetscCall(PetscMalloc1(nsplit, &jac->Afield));
777: for (i = 0; i < nsplit; i++) {
778: if (jac->offdiag_use_amat) {
779: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
780: } else {
781: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
782: }
783: ilink = ilink->next;
784: }
785: } else {
786: MatReuse scall;
787: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
788: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
789: scall = MAT_INITIAL_MATRIX;
790: } else scall = MAT_REUSE_MATRIX;
792: for (i = 0; i < nsplit; i++) {
793: if (jac->offdiag_use_amat) {
794: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
795: } else {
796: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
797: }
798: ilink = ilink->next;
799: }
800: }
801: }
802: }
804: if (jac->type == PC_COMPOSITE_SCHUR) {
805: IS ccis;
806: PetscBool isset, isspd;
807: PetscInt rstart, rend;
808: char lscname[256];
809: PetscObject LSC_L;
810: PetscBool set, flg;
812: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields");
814: /* If pc->mat is SPD, don't scale by -1 the Schur complement */
815: if (jac->schurscale == (PetscScalar)-1.0) {
816: PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
817: jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
818: }
820: /* When extracting off-diagonal submatrices, we take complements from this range */
821: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
822: PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
824: if (jac->schur) {
825: KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
826: MatReuse scall;
828: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
829: scall = MAT_INITIAL_MATRIX;
830: PetscCall(MatDestroy(&jac->B));
831: PetscCall(MatDestroy(&jac->C));
832: } else scall = MAT_REUSE_MATRIX;
834: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
835: ilink = jac->head;
836: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
837: if (jac->offdiag_use_amat) {
838: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
839: } else {
840: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
841: }
842: PetscCall(ISDestroy(&ccis));
843: if (!flg) {
844: ilink = ilink->next;
845: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
846: if (jac->offdiag_use_amat) {
847: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
848: } else {
849: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
850: }
851: PetscCall(ISDestroy(&ccis));
852: } else {
853: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
854: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
855: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
856: }
857: PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
858: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
859: PetscCall(MatDestroy(&jac->schurp));
860: PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
861: }
862: if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
863: if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
864: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
865: } else {
866: const char *Dprefix;
867: char schurprefix[256], schurmatprefix[256];
868: char schurtestoption[256];
869: MatNullSpace sp;
870: KSP kspt;
872: /* extract the A01 and A10 matrices */
873: ilink = jac->head;
874: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
875: if (jac->offdiag_use_amat) {
876: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
877: } else {
878: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
879: }
880: PetscCall(ISDestroy(&ccis));
881: ilink = ilink->next;
882: if (!flg) {
883: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
884: if (jac->offdiag_use_amat) {
885: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
886: } else {
887: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
888: }
889: PetscCall(ISDestroy(&ccis));
890: } else {
891: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
892: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
893: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
894: }
895: /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
896: PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
897: PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
898: PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
899: PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
900: PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
901: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
902: PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));
904: /* Note: this is not true in general */
905: PetscCall(MatGetNullSpace(jac->mat[1], &sp));
906: if (sp) PetscCall(MatSetNullSpace(jac->schur, sp));
908: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
909: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
910: if (flg) {
911: DM dmInner;
912: KSP kspInner;
913: PC pcInner;
915: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
916: PetscCall(KSPReset(kspInner));
917: PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
918: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
919: /* Indent this deeper to emphasize the "inner" nature of this solver. */
920: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
921: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
922: PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));
924: /* Set DM for new solver */
925: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
926: PetscCall(KSPSetDM(kspInner, dmInner));
927: PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));
929: /* Defaults to PCKSP as preconditioner */
930: PetscCall(KSPGetPC(kspInner, &pcInner));
931: PetscCall(PCSetType(pcInner, PCKSP));
932: PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
933: } else {
934: /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
935: * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
936: * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
937: * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
938: * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
939: * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
940: PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
941: PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
942: }
943: PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
944: PetscCall(KSPSetFromOptions(jac->head->ksp));
945: PetscCall(MatSetFromOptions(jac->schur));
947: PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg));
948: if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */
949: KSP kspInner;
950: PC pcInner;
952: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
953: PetscCall(KSPGetPC(kspInner, &pcInner));
954: PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
955: if (flg) {
956: KSP ksp;
958: PetscCall(PCKSPGetKSP(pcInner, &ksp));
959: if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
960: }
961: }
962: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
963: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
964: if (flg) {
965: DM dmInner;
967: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
968: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
969: PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
970: PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
971: PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
972: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
973: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
974: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
975: PetscCall(KSPSetDM(jac->kspupper, dmInner));
976: PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
977: PetscCall(KSPSetFromOptions(jac->kspupper));
978: PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
979: PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
980: } else {
981: jac->kspupper = jac->head->ksp;
982: PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
983: }
985: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
986: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
987: PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
988: PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
989: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
990: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
991: PC pcschur;
992: PetscCall(KSPGetPC(jac->kspschur, &pcschur));
993: PetscCall(PCSetType(pcschur, PCNONE));
994: /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
995: } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
996: PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
997: }
998: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
999: PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1000: PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1001: /* propagate DM */
1002: {
1003: DM sdm;
1004: PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1005: if (sdm) {
1006: PetscCall(KSPSetDM(jac->kspschur, sdm));
1007: PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1008: }
1009: }
1010: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1011: /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1012: PetscCall(KSPSetFromOptions(jac->kspschur));
1013: }
1014: PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1015: PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1017: /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1018: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1019: PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1020: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1021: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1022: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1023: PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1024: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1025: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1026: } else if (jac->type == PC_COMPOSITE_GKB) {
1027: IS ccis;
1028: PetscInt rstart, rend;
1030: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1032: ilink = jac->head;
1034: /* When extracting off-diagonal submatrices, we take complements from this range */
1035: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
1037: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1038: if (jac->offdiag_use_amat) {
1039: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1040: } else {
1041: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1042: }
1043: PetscCall(ISDestroy(&ccis));
1044: /* Create work vectors for GKB algorithm */
1045: PetscCall(VecDuplicate(ilink->x, &jac->u));
1046: PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1047: PetscCall(VecDuplicate(ilink->x, &jac->w2));
1048: ilink = ilink->next;
1049: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1050: if (jac->offdiag_use_amat) {
1051: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1052: } else {
1053: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1054: }
1055: PetscCall(ISDestroy(&ccis));
1056: /* Create work vectors for GKB algorithm */
1057: PetscCall(VecDuplicate(ilink->x, &jac->v));
1058: PetscCall(VecDuplicate(ilink->x, &jac->d));
1059: PetscCall(VecDuplicate(ilink->x, &jac->w1));
1060: PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1061: PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));
1063: ilink = jac->head;
1064: PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1065: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1066: /* Create gkb_monitor context */
1067: if (jac->gkbmonitor) {
1068: PetscInt tablevel;
1069: PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1070: PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1071: PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1072: PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1073: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1074: }
1075: } else {
1076: /* set up the individual splits' PCs */
1077: i = 0;
1078: ilink = jac->head;
1079: while (ilink) {
1080: PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1081: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1082: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1083: i++;
1084: ilink = ilink->next;
1085: }
1086: }
1088: /* Set coordinates to the sub PC objects whenever these are set */
1089: if (jac->coordinates_set) {
1090: PC pc_coords;
1091: if (jac->type == PC_COMPOSITE_SCHUR) {
1092: // Head is first block.
1093: PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1094: PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1095: // Second one is Schur block, but its KSP object is in kspschur.
1096: PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1097: PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1098: } else if (jac->type == PC_COMPOSITE_GKB) {
1099: PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1100: } else {
1101: ilink = jac->head;
1102: while (ilink) {
1103: PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1104: PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1105: ilink = ilink->next;
1106: }
1107: }
1108: }
1110: jac->suboptionsset = PETSC_TRUE;
1111: PetscFunctionReturn(PETSC_SUCCESS);
1112: }
1114: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1115: ((PetscErrorCode)(VecScatterBegin(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || VecScatterEnd(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || \
1116: KSPSolve(ilink->ksp, ilink->x, ilink->y) || KSPCheckSolve(ilink->ksp, pc, ilink->y) || PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || VecScatterBegin(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE) || \
1117: VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))
1119: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1120: {
1121: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1122: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1123: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1125: PetscFunctionBegin;
1126: switch (jac->schurfactorization) {
1127: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1128: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1129: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1130: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1131: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1132: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1133: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1134: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1135: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1136: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1137: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1138: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1139: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1140: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1141: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1142: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1143: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1144: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1145: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1146: break;
1147: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1148: /* [A00 0; A10 S], suitable for left preconditioning */
1149: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1150: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1151: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1152: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1153: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1154: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1155: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1156: PetscCall(VecScale(ilinkD->x, -1.));
1157: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1158: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1159: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1160: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1161: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1162: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1163: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1164: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1165: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1166: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1167: break;
1168: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1169: /* [A00 A01; 0 S], suitable for right preconditioning */
1170: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1171: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1172: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1173: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1174: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1175: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1176: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1177: PetscCall(VecScale(ilinkA->x, -1.));
1178: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1179: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1180: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1181: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1182: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1183: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1184: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1185: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1186: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1187: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1188: break;
1189: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1190: /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1191: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1192: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1193: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1194: PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1195: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1196: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1197: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1198: PetscCall(VecScale(ilinkD->x, -1.0));
1199: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1200: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1202: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1203: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1204: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1205: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1206: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1208: if (kspUpper == kspA) {
1209: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1210: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1211: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1212: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1213: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1214: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1215: } else {
1216: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1217: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1218: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1219: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1220: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1221: PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1222: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1223: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1224: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1225: }
1226: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1227: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1228: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1229: }
1230: PetscFunctionReturn(PETSC_SUCCESS);
1231: }
1233: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1234: {
1235: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1236: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1237: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1239: PetscFunctionBegin;
1240: switch (jac->schurfactorization) {
1241: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1242: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1243: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1244: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1245: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1246: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1247: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1248: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1249: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1250: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1252: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1253: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1254: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1255: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1256: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1257: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1258: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1259: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1260: break;
1261: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1262: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1263: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1264: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1265: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1266: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1267: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1268: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1269: PetscCall(VecScale(ilinkD->x, -1.));
1270: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1271: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1272: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1273: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1274: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1275: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1276: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1278: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1279: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1280: break;
1281: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1282: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1283: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1284: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1285: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1286: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1287: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1288: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1289: PetscCall(VecScale(ilinkA->x, -1.));
1290: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1291: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1292: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1293: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1294: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1295: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1296: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1297: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1298: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1299: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1300: break;
1301: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1302: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1303: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1304: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1305: PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1306: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1307: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1308: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1309: PetscCall(VecScale(ilinkD->x, -1.0));
1310: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1311: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1313: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1314: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1315: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1316: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1317: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1319: if (kspLower == kspA) {
1320: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1321: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1322: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1323: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1324: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1325: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1326: } else {
1327: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1328: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1329: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1330: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1331: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1332: PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1333: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1334: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1335: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1336: }
1337: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1338: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1339: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1340: }
1341: PetscFunctionReturn(PETSC_SUCCESS);
1342: }
1344: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1345: {
1346: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1347: PC_FieldSplitLink ilink = jac->head;
1348: PetscInt cnt, bs;
1350: PetscFunctionBegin;
1351: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1352: if (jac->defaultsplit) {
1353: PetscCall(VecGetBlockSize(x, &bs));
1354: PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of x vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1355: PetscCall(VecGetBlockSize(y, &bs));
1356: PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of y vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1357: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1358: while (ilink) {
1359: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1360: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1361: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1362: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1363: ilink = ilink->next;
1364: }
1365: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1366: } else {
1367: PetscCall(VecSet(y, 0.0));
1368: while (ilink) {
1369: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1370: ilink = ilink->next;
1371: }
1372: }
1373: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1374: PetscCall(VecSet(y, 0.0));
1375: /* solve on first block for first block variables */
1376: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1377: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1378: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1379: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1380: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1381: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1382: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1383: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1385: /* compute the residual only onto second block variables using first block variables */
1386: PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1387: ilink = ilink->next;
1388: PetscCall(VecScale(ilink->x, -1.0));
1389: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1390: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1392: /* solve on second block variables */
1393: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1394: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1395: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1396: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1397: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1398: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1399: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1400: if (!jac->w1) {
1401: PetscCall(VecDuplicate(x, &jac->w1));
1402: PetscCall(VecDuplicate(x, &jac->w2));
1403: }
1404: PetscCall(VecSet(y, 0.0));
1405: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1406: cnt = 1;
1407: while (ilink->next) {
1408: ilink = ilink->next;
1409: /* compute the residual only over the part of the vector needed */
1410: PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1411: PetscCall(VecScale(ilink->x, -1.0));
1412: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1413: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1414: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1415: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1416: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1417: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1418: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1419: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1420: }
1421: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1422: cnt -= 2;
1423: while (ilink->previous) {
1424: ilink = ilink->previous;
1425: /* compute the residual only over the part of the vector needed */
1426: PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1427: PetscCall(VecScale(ilink->x, -1.0));
1428: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1429: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1430: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1431: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1432: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1433: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1434: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1435: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1436: }
1437: }
1438: } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1439: PetscFunctionReturn(PETSC_SUCCESS);
1440: }
1442: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1443: {
1444: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1445: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1446: KSP ksp = ilinkA->ksp;
1447: Vec u, v, Hu, d, work1, work2;
1448: PetscScalar alpha, z, nrmz2, *vecz;
1449: PetscReal lowbnd, nu, beta;
1450: PetscInt j, iterGKB;
1452: PetscFunctionBegin;
1453: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1454: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1455: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1456: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1458: u = jac->u;
1459: v = jac->v;
1460: Hu = jac->Hu;
1461: d = jac->d;
1462: work1 = jac->w1;
1463: work2 = jac->w2;
1464: vecz = jac->vecz;
1466: /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1467: /* Add q = q + nu*B*b */
1468: if (jac->gkbnu) {
1469: nu = jac->gkbnu;
1470: PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1471: PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1472: } else {
1473: /* Situation when no augmented Lagrangian is used. Then we set inner */
1474: /* matrix N = I in [Ar13], and thus nu = 1. */
1475: nu = 1;
1476: }
1478: /* Transform rhs from [q,tilde{b}] to [0,b] */
1479: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1480: PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1481: PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1482: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1483: PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1484: PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x */
1486: /* First step of algorithm */
1487: PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1488: KSPCheckDot(ksp, beta);
1489: beta = PetscSqrtReal(nu) * beta;
1490: PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c */
1491: PetscCall(MatMult(jac->B, v, work2)); /* u = H^{-1}*B*v */
1492: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1493: PetscCall(KSPSolve(ksp, work2, u));
1494: PetscCall(KSPCheckSolve(ksp, pc, u));
1495: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1496: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1497: PetscCall(VecDot(Hu, u, &alpha));
1498: KSPCheckDot(ksp, alpha);
1499: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1500: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1501: PetscCall(VecScale(u, 1.0 / alpha));
1502: PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c */
1504: z = beta / alpha;
1505: vecz[1] = z;
1507: /* Computation of first iterate x(1) and p(1) */
1508: PetscCall(VecAXPY(ilinkA->y, z, u));
1509: PetscCall(VecCopy(d, ilinkD->y));
1510: PetscCall(VecScale(ilinkD->y, -z));
1512: iterGKB = 1;
1513: lowbnd = 2 * jac->gkbtol;
1514: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1516: while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1517: iterGKB += 1;
1518: PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1519: PetscCall(VecAXPBY(v, nu, -alpha, work1));
1520: PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v */
1521: beta = beta / PetscSqrtReal(nu);
1522: PetscCall(VecScale(v, 1.0 / beta));
1523: PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1524: PetscCall(MatMult(jac->H, u, Hu));
1525: PetscCall(VecAXPY(work2, -beta, Hu));
1526: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1527: PetscCall(KSPSolve(ksp, work2, u));
1528: PetscCall(KSPCheckSolve(ksp, pc, u));
1529: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1530: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1531: PetscCall(VecDot(Hu, u, &alpha));
1532: KSPCheckDot(ksp, alpha);
1533: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1534: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1535: PetscCall(VecScale(u, 1.0 / alpha));
1537: z = -beta / alpha * z; /* z <- beta/alpha*z */
1538: vecz[0] = z;
1540: /* Computation of new iterate x(i+1) and p(i+1) */
1541: PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1542: PetscCall(VecAXPY(ilinkA->y, z, u)); /* r = r + z*u */
1543: PetscCall(VecAXPY(ilinkD->y, -z, d)); /* p = p - z*d */
1544: PetscCall(MatMult(jac->H, ilinkA->y, Hu)); /* ||u||_H = u'*H*u */
1545: PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));
1547: /* Compute Lower Bound estimate */
1548: if (iterGKB > jac->gkbdelay) {
1549: lowbnd = 0.0;
1550: for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1551: lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1552: }
1554: for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1555: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1556: }
1558: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1559: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1560: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1561: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1562: PetscFunctionReturn(PETSC_SUCCESS);
1563: }
1565: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1566: ((PetscErrorCode)(VecScatterBegin(ilink->sctx, xx, ilink->y, INSERT_VALUES, SCATTER_FORWARD) || VecScatterEnd(ilink->sctx, xx, ilink->y, INSERT_VALUES, SCATTER_FORWARD) || PetscLogEventBegin(ilink->event, ilink->ksp, ilink->y, ilink->x, NULL) || \
1567: KSPSolveTranspose(ilink->ksp, ilink->y, ilink->x) || KSPCheckSolve(ilink->ksp, pc, ilink->x) || PetscLogEventEnd(ilink->event, ilink->ksp, ilink->y, ilink->x, NULL) || VecScatterBegin(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE) || \
1568: VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))
1570: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1571: {
1572: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1573: PC_FieldSplitLink ilink = jac->head;
1574: PetscInt bs;
1576: PetscFunctionBegin;
1577: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1578: if (jac->defaultsplit) {
1579: PetscCall(VecGetBlockSize(x, &bs));
1580: PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of x vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1581: PetscCall(VecGetBlockSize(y, &bs));
1582: PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of y vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1583: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1584: while (ilink) {
1585: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1586: PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1587: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1588: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1589: ilink = ilink->next;
1590: }
1591: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1592: } else {
1593: PetscCall(VecSet(y, 0.0));
1594: while (ilink) {
1595: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1596: ilink = ilink->next;
1597: }
1598: }
1599: } else {
1600: if (!jac->w1) {
1601: PetscCall(VecDuplicate(x, &jac->w1));
1602: PetscCall(VecDuplicate(x, &jac->w2));
1603: }
1604: PetscCall(VecSet(y, 0.0));
1605: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1606: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1607: while (ilink->next) {
1608: ilink = ilink->next;
1609: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1610: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1611: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1612: }
1613: while (ilink->previous) {
1614: ilink = ilink->previous;
1615: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1616: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1617: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1618: }
1619: } else {
1620: while (ilink->next) { /* get to last entry in linked list */
1621: ilink = ilink->next;
1622: }
1623: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1624: while (ilink->previous) {
1625: ilink = ilink->previous;
1626: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1627: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1628: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1629: }
1630: }
1631: }
1632: PetscFunctionReturn(PETSC_SUCCESS);
1633: }
1635: static PetscErrorCode PCReset_FieldSplit(PC pc)
1636: {
1637: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1638: PC_FieldSplitLink ilink = jac->head, next;
1640: PetscFunctionBegin;
1641: while (ilink) {
1642: PetscCall(KSPDestroy(&ilink->ksp));
1643: PetscCall(VecDestroy(&ilink->x));
1644: PetscCall(VecDestroy(&ilink->y));
1645: PetscCall(VecDestroy(&ilink->z));
1646: PetscCall(VecScatterDestroy(&ilink->sctx));
1647: PetscCall(ISDestroy(&ilink->is));
1648: PetscCall(ISDestroy(&ilink->is_col));
1649: PetscCall(PetscFree(ilink->splitname));
1650: PetscCall(PetscFree(ilink->fields));
1651: PetscCall(PetscFree(ilink->fields_col));
1652: next = ilink->next;
1653: PetscCall(PetscFree(ilink));
1654: ilink = next;
1655: }
1656: jac->head = NULL;
1657: PetscCall(PetscFree2(jac->x, jac->y));
1658: if (jac->mat && jac->mat != jac->pmat) {
1659: PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1660: } else if (jac->mat) {
1661: jac->mat = NULL;
1662: }
1663: if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1664: if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1665: jac->nsplits = 0;
1666: PetscCall(VecDestroy(&jac->w1));
1667: PetscCall(VecDestroy(&jac->w2));
1668: PetscCall(MatDestroy(&jac->schur));
1669: PetscCall(MatDestroy(&jac->schurp));
1670: PetscCall(MatDestroy(&jac->schur_user));
1671: PetscCall(KSPDestroy(&jac->kspschur));
1672: PetscCall(KSPDestroy(&jac->kspupper));
1673: PetscCall(MatDestroy(&jac->B));
1674: PetscCall(MatDestroy(&jac->C));
1675: PetscCall(MatDestroy(&jac->H));
1676: PetscCall(VecDestroy(&jac->u));
1677: PetscCall(VecDestroy(&jac->v));
1678: PetscCall(VecDestroy(&jac->Hu));
1679: PetscCall(VecDestroy(&jac->d));
1680: PetscCall(PetscFree(jac->vecz));
1681: PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1682: jac->isrestrict = PETSC_FALSE;
1683: PetscFunctionReturn(PETSC_SUCCESS);
1684: }
1686: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1687: {
1688: PetscFunctionBegin;
1689: PetscCall(PCReset_FieldSplit(pc));
1690: PetscCall(PetscFree(pc->data));
1691: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1692: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1693: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1694: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1695: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1696: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1697: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1698: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1700: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1701: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1702: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1703: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1704: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1705: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1706: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1707: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1708: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1709: PetscFunctionReturn(PETSC_SUCCESS);
1710: }
1712: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1713: {
1714: PetscInt bs;
1715: PetscBool flg;
1716: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1717: PCCompositeType ctype;
1719: PetscFunctionBegin;
1720: PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1721: PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1722: PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1723: if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1724: jac->diag_use_amat = pc->useAmat;
1725: PetscCall(PetscOptionsBool("-pc_fieldsplit_diag_use_amat", "Use Amat (not Pmat) to extract diagonal fieldsplit blocks", "PCFieldSplitSetDiagUseAmat", jac->diag_use_amat, &jac->diag_use_amat, NULL));
1726: jac->offdiag_use_amat = pc->useAmat;
1727: PetscCall(PetscOptionsBool("-pc_fieldsplit_off_diag_use_amat", "Use Amat (not Pmat) to extract off-diagonal fieldsplit blocks", "PCFieldSplitSetOffDiagUseAmat", jac->offdiag_use_amat, &jac->offdiag_use_amat, NULL));
1728: PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1729: PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1730: PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1731: if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1732: /* Only setup fields once */
1733: if ((jac->bs > 0) && (jac->nsplits == 0)) {
1734: /* only allow user to set fields from command line if bs is already known.
1735: otherwise user can set them in PCFieldSplitSetDefaults() */
1736: PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1737: if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1738: }
1739: if (jac->type == PC_COMPOSITE_SCHUR) {
1740: PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1741: if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1742: PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_fact_type", "Which off-diagonal parts of the block factorization to use", "PCFieldSplitSetSchurFactType", PCFieldSplitSchurFactTypes, (PetscEnum)jac->schurfactorization, (PetscEnum *)&jac->schurfactorization, NULL));
1743: PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1744: PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1745: } else if (jac->type == PC_COMPOSITE_GKB) {
1746: PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1747: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1748: PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1749: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1750: PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1751: }
1752: /*
1753: In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1754: But after the initial setup of ALL the layers of sub-solvers is completed we do want to call KSPSetFromOptions() on the sub-solvers every time it
1755: is called on the outer solver in case changes were made in the options database
1757: But even after PCSetUp_FieldSplit() is called all the options inside the inner levels of sub-solvers may still not have been set thus we only call the KSPSetFromOptions()
1758: if we know that the entire stack of sub-solvers below this have been complete instantiated, we check this by seeing if any solver iterations are complete.
1759: Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.
1761: There could be a negative side effect of calling the KSPSetFromOptions() below.
1763: If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1764: */
1765: if (jac->issetup) {
1766: PC_FieldSplitLink ilink = jac->head;
1767: if (jac->type == PC_COMPOSITE_SCHUR) {
1768: if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1769: if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1770: }
1771: while (ilink) {
1772: if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1773: ilink = ilink->next;
1774: }
1775: }
1776: PetscOptionsHeadEnd();
1777: PetscFunctionReturn(PETSC_SUCCESS);
1778: }
1780: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1781: {
1782: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1783: PC_FieldSplitLink ilink, next = jac->head;
1784: char prefix[128];
1785: PetscInt i;
1787: PetscFunctionBegin;
1788: if (jac->splitdefined) {
1789: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1790: PetscFunctionReturn(PETSC_SUCCESS);
1791: }
1792: for (i = 0; i < n; i++) {
1793: PetscCheck(fields[i] < jac->bs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", fields[i], jac->bs);
1794: PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1795: }
1796: PetscCall(PetscNew(&ilink));
1797: if (splitname) {
1798: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1799: } else {
1800: PetscCall(PetscMalloc1(3, &ilink->splitname));
1801: PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1802: }
1803: ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1804: PetscCall(PetscMalloc1(n, &ilink->fields));
1805: PetscCall(PetscArraycpy(ilink->fields, fields, n));
1806: PetscCall(PetscMalloc1(n, &ilink->fields_col));
1807: PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));
1809: ilink->nfields = n;
1810: ilink->next = NULL;
1811: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1812: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1813: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1814: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1815: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1817: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1818: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1820: if (!next) {
1821: jac->head = ilink;
1822: ilink->previous = NULL;
1823: } else {
1824: while (next->next) next = next->next;
1825: next->next = ilink;
1826: ilink->previous = next;
1827: }
1828: jac->nsplits++;
1829: PetscFunctionReturn(PETSC_SUCCESS);
1830: }
1832: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1833: {
1834: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1836: PetscFunctionBegin;
1837: *subksp = NULL;
1838: if (n) *n = 0;
1839: if (jac->type == PC_COMPOSITE_SCHUR) {
1840: PetscInt nn;
1842: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1843: PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1844: nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1845: PetscCall(PetscMalloc1(nn, subksp));
1846: (*subksp)[0] = jac->head->ksp;
1847: (*subksp)[1] = jac->kspschur;
1848: if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1849: if (n) *n = nn;
1850: }
1851: PetscFunctionReturn(PETSC_SUCCESS);
1852: }
1854: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1855: {
1856: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1858: PetscFunctionBegin;
1859: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1860: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1861: PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));
1863: (*subksp)[1] = jac->kspschur;
1864: if (n) *n = jac->nsplits;
1865: PetscFunctionReturn(PETSC_SUCCESS);
1866: }
1868: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1869: {
1870: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1871: PetscInt cnt = 0;
1872: PC_FieldSplitLink ilink = jac->head;
1874: PetscFunctionBegin;
1875: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1876: while (ilink) {
1877: (*subksp)[cnt++] = ilink->ksp;
1878: ilink = ilink->next;
1879: }
1880: PetscCheck(cnt == jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Corrupt PCFIELDSPLIT object: number of splits in linked list %" PetscInt_FMT " does not match number in object %" PetscInt_FMT, cnt, jac->nsplits);
1881: if (n) *n = jac->nsplits;
1882: PetscFunctionReturn(PETSC_SUCCESS);
1883: }
1885: /*@C
1886: PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.
1888: Input Parameters:
1889: + pc - the preconditioner context
1890: - isy - the index set that defines the indices to which the fieldsplit is to be restricted
1892: Level: advanced
1894: Developer Notes:
1895: It seems the resulting `IS`s will not cover the entire space, so
1896: how can they define a convergent preconditioner? Needs explaining.
1898: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1899: @*/
1900: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1901: {
1902: PetscFunctionBegin;
1905: PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1906: PetscFunctionReturn(PETSC_SUCCESS);
1907: }
1909: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1910: {
1911: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1912: PC_FieldSplitLink ilink = jac->head, next;
1913: PetscInt localsize, size, sizez, i;
1914: const PetscInt *ind, *indz;
1915: PetscInt *indc, *indcz;
1916: PetscBool flg;
1918: PetscFunctionBegin;
1919: PetscCall(ISGetLocalSize(isy, &localsize));
1920: PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1921: size -= localsize;
1922: while (ilink) {
1923: IS isrl, isr;
1924: PC subpc;
1925: PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1926: PetscCall(ISGetLocalSize(isrl, &localsize));
1927: PetscCall(PetscMalloc1(localsize, &indc));
1928: PetscCall(ISGetIndices(isrl, &ind));
1929: PetscCall(PetscArraycpy(indc, ind, localsize));
1930: PetscCall(ISRestoreIndices(isrl, &ind));
1931: PetscCall(ISDestroy(&isrl));
1932: for (i = 0; i < localsize; i++) *(indc + i) += size;
1933: PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1934: PetscCall(PetscObjectReference((PetscObject)isr));
1935: PetscCall(ISDestroy(&ilink->is));
1936: ilink->is = isr;
1937: PetscCall(PetscObjectReference((PetscObject)isr));
1938: PetscCall(ISDestroy(&ilink->is_col));
1939: ilink->is_col = isr;
1940: PetscCall(ISDestroy(&isr));
1941: PetscCall(KSPGetPC(ilink->ksp, &subpc));
1942: PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1943: if (flg) {
1944: IS iszl, isz;
1945: MPI_Comm comm;
1946: PetscCall(ISGetLocalSize(ilink->is, &localsize));
1947: comm = PetscObjectComm((PetscObject)ilink->is);
1948: PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1949: PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1950: sizez -= localsize;
1951: PetscCall(ISGetLocalSize(iszl, &localsize));
1952: PetscCall(PetscMalloc1(localsize, &indcz));
1953: PetscCall(ISGetIndices(iszl, &indz));
1954: PetscCall(PetscArraycpy(indcz, indz, localsize));
1955: PetscCall(ISRestoreIndices(iszl, &indz));
1956: PetscCall(ISDestroy(&iszl));
1957: for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1958: PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1959: PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1960: PetscCall(ISDestroy(&isz));
1961: }
1962: next = ilink->next;
1963: ilink = next;
1964: }
1965: jac->isrestrict = PETSC_TRUE;
1966: PetscFunctionReturn(PETSC_SUCCESS);
1967: }
1969: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1970: {
1971: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1972: PC_FieldSplitLink ilink, next = jac->head;
1973: char prefix[128];
1975: PetscFunctionBegin;
1976: if (jac->splitdefined) {
1977: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1978: PetscFunctionReturn(PETSC_SUCCESS);
1979: }
1980: PetscCall(PetscNew(&ilink));
1981: if (splitname) {
1982: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1983: } else {
1984: PetscCall(PetscMalloc1(8, &ilink->splitname));
1985: PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1986: }
1987: ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1988: PetscCall(PetscObjectReference((PetscObject)is));
1989: PetscCall(ISDestroy(&ilink->is));
1990: ilink->is = is;
1991: PetscCall(PetscObjectReference((PetscObject)is));
1992: PetscCall(ISDestroy(&ilink->is_col));
1993: ilink->is_col = is;
1994: ilink->next = NULL;
1995: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1996: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1997: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1998: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1999: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
2001: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2002: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
2004: if (!next) {
2005: jac->head = ilink;
2006: ilink->previous = NULL;
2007: } else {
2008: while (next->next) next = next->next;
2009: next->next = ilink;
2010: ilink->previous = next;
2011: }
2012: jac->nsplits++;
2013: PetscFunctionReturn(PETSC_SUCCESS);
2014: }
2016: /*@C
2017: PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`
2019: Logically Collective
2021: Input Parameters:
2022: + pc - the preconditioner context
2023: . splitname - name of this split, if `NULL` the number of the split is used
2024: . n - the number of fields in this split
2025: . fields - the fields in this split
2026: - fields_col - generally the same as fields, if it does not match fields then the matrix block that is solved for this set of fields comes from an off-diagonal block
2027: of the matrix and fields_col provides the column indices for that block
2029: Level: intermediate
2031: Notes:
2032: Use `PCFieldSplitSetIS()` to set a general set of indices as a split.
2034: `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2035: size is three then one can define a split as 0, or 1 or 2 or 0,1 or 0,2 or 1,2 which mean
2036: 0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2037: where the numbered entries indicate what is in the split.
2039: This function is called once per split (it creates a new split each time). Solve options
2040: for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.
2042: `PCFieldSplitSetIS()` does not support having a fields_col different from fields
2044: Developer Notes:
2045: This routine does not actually create the `IS` representing the split, that is delayed
2046: until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2047: available when this routine is called.
2049: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2050: @*/
2051: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2052: {
2053: PetscFunctionBegin;
2055: PetscAssertPointer(splitname, 2);
2056: PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2057: PetscAssertPointer(fields, 4);
2058: PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2059: PetscFunctionReturn(PETSC_SUCCESS);
2060: }
2062: /*@
2063: PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2064: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2066: Logically Collective
2068: Input Parameters:
2069: + pc - the preconditioner object
2070: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2072: Options Database Key:
2073: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks
2075: Level: intermediate
2077: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2078: @*/
2079: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2080: {
2081: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2082: PetscBool isfs;
2084: PetscFunctionBegin;
2086: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2087: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2088: jac->diag_use_amat = flg;
2089: PetscFunctionReturn(PETSC_SUCCESS);
2090: }
2092: /*@
2093: PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2094: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2096: Logically Collective
2098: Input Parameter:
2099: . pc - the preconditioner object
2101: Output Parameter:
2102: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2104: Level: intermediate
2106: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2107: @*/
2108: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2109: {
2110: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2111: PetscBool isfs;
2113: PetscFunctionBegin;
2115: PetscAssertPointer(flg, 2);
2116: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2117: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2118: *flg = jac->diag_use_amat;
2119: PetscFunctionReturn(PETSC_SUCCESS);
2120: }
2122: /*@
2123: PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2124: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2126: Logically Collective
2128: Input Parameters:
2129: + pc - the preconditioner object
2130: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2132: Options Database Key:
2133: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks
2135: Level: intermediate
2137: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2138: @*/
2139: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2140: {
2141: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2142: PetscBool isfs;
2144: PetscFunctionBegin;
2146: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2147: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2148: jac->offdiag_use_amat = flg;
2149: PetscFunctionReturn(PETSC_SUCCESS);
2150: }
2152: /*@
2153: PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2154: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2156: Logically Collective
2158: Input Parameter:
2159: . pc - the preconditioner object
2161: Output Parameter:
2162: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2164: Level: intermediate
2166: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2167: @*/
2168: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2169: {
2170: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2171: PetscBool isfs;
2173: PetscFunctionBegin;
2175: PetscAssertPointer(flg, 2);
2176: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2177: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2178: *flg = jac->offdiag_use_amat;
2179: PetscFunctionReturn(PETSC_SUCCESS);
2180: }
2182: /*@C
2183: PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`
2185: Logically Collective
2187: Input Parameters:
2188: + pc - the preconditioner context
2189: . splitname - name of this split, if `NULL` the number of the split is used
2190: - is - the index set that defines the elements in this split
2192: Level: intermediate
2194: Notes:
2195: Use `PCFieldSplitSetFields()`, for splits defined by strided types.
2197: This function is called once per split (it creates a new split each time). Solve options
2198: for this split will be available under the prefix -fieldsplit_SPLITNAME_.
2200: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2201: @*/
2202: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2203: {
2204: PetscFunctionBegin;
2206: if (splitname) PetscAssertPointer(splitname, 2);
2208: PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2209: PetscFunctionReturn(PETSC_SUCCESS);
2210: }
2212: /*@C
2213: PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`
2215: Logically Collective
2217: Input Parameters:
2218: + pc - the preconditioner context
2219: - splitname - name of this split
2221: Output Parameter:
2222: . is - the index set that defines the elements in this split, or `NULL` if the split is not found
2224: Level: intermediate
2226: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2227: @*/
2228: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2229: {
2230: PetscFunctionBegin;
2232: PetscAssertPointer(splitname, 2);
2233: PetscAssertPointer(is, 3);
2234: {
2235: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2236: PC_FieldSplitLink ilink = jac->head;
2237: PetscBool found;
2239: *is = NULL;
2240: while (ilink) {
2241: PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2242: if (found) {
2243: *is = ilink->is;
2244: break;
2245: }
2246: ilink = ilink->next;
2247: }
2248: }
2249: PetscFunctionReturn(PETSC_SUCCESS);
2250: }
2252: /*@C
2253: PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`
2255: Logically Collective
2257: Input Parameters:
2258: + pc - the preconditioner context
2259: - index - index of this split
2261: Output Parameter:
2262: . is - the index set that defines the elements in this split
2264: Level: intermediate
2266: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2267: @*/
2268: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2269: {
2270: PetscFunctionBegin;
2271: PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2273: PetscAssertPointer(is, 3);
2274: {
2275: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2276: PC_FieldSplitLink ilink = jac->head;
2277: PetscInt i = 0;
2278: PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);
2280: while (i < index) {
2281: ilink = ilink->next;
2282: ++i;
2283: }
2284: PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2285: }
2286: PetscFunctionReturn(PETSC_SUCCESS);
2287: }
2289: /*@
2290: PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2291: fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.
2293: Logically Collective
2295: Input Parameters:
2296: + pc - the preconditioner context
2297: - bs - the block size
2299: Level: intermediate
2301: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2302: @*/
2303: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2304: {
2305: PetscFunctionBegin;
2308: PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2309: PetscFunctionReturn(PETSC_SUCCESS);
2310: }
2312: /*@C
2313: PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits
2315: Collective
2317: Input Parameter:
2318: . pc - the preconditioner context
2320: Output Parameters:
2321: + n - the number of splits
2322: - subksp - the array of `KSP` contexts
2324: Level: advanced
2326: Notes:
2327: After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2328: (not the `KSP`, just the array that contains them).
2330: You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.
2332: If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2333: Schur complement and the `KSP` object used to iterate over the Schur complement.
2334: To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.
2336: If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2337: inner linear system defined by the matrix H in each loop.
2339: Fortran Notes:
2340: You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2341: You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2342: `KSP` array must be.
2344: Developer Notes:
2345: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2347: The Fortran interface should be modernized to return directly the array of values.
2349: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2350: @*/
2351: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2352: {
2353: PetscFunctionBegin;
2355: if (n) PetscAssertPointer(n, 2);
2356: PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2357: PetscFunctionReturn(PETSC_SUCCESS);
2358: }
2360: /*@C
2361: PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`
2363: Collective
2365: Input Parameter:
2366: . pc - the preconditioner context
2368: Output Parameters:
2369: + n - the number of splits
2370: - subksp - the array of `KSP` contexts
2372: Level: advanced
2374: Notes:
2375: After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2376: (not the `KSP` just the array that contains them).
2378: You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.
2380: If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2381: + 1 - the `KSP` used for the (1,1) block
2382: . 2 - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2383: - 3 - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).
2385: It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.
2387: Fortran Notes:
2388: You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2389: You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2390: `KSP` array must be.
2392: Developer Notes:
2393: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2395: Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?
2397: The Fortran interface should be modernized to return directly the array of values.
2399: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2400: @*/
2401: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2402: {
2403: PetscFunctionBegin;
2405: if (n) PetscAssertPointer(n, 2);
2406: PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2407: PetscFunctionReturn(PETSC_SUCCESS);
2408: }
2410: /*@
2411: PCFieldSplitSetSchurPre - Indicates from what operator the preconditioner is constructed for the Schur complement.
2412: The default is the A11 matrix.
2414: Collective
2416: Input Parameters:
2417: + pc - the preconditioner context
2418: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2419: `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2420: `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2421: - pre - matrix to use for preconditioning, or `NULL`
2423: Options Database Keys:
2424: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2425: - -fieldsplit_1_pc_type <pctype> - the preconditioner algorithm that is used to construct the preconditioner from the operator
2427: Level: intermediate
2429: Notes:
2430: If ptype is
2431: + a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2432: matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2433: . self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2434: The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2435: . user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2436: to this function).
2437: . selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2438: This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2439: lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2440: - full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2441: computed internally by `PCFIELDSPLIT` (this is expensive)
2442: useful mostly as a test that the Schur complement approach can work for your problem
2444: When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2445: with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2446: `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.
2448: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2449: `MatSchurComplementSetAinvType()`, `PCLSC`
2451: @*/
2452: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2453: {
2454: PetscFunctionBegin;
2456: PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2457: PetscFunctionReturn(PETSC_SUCCESS);
2458: }
2460: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2461: {
2462: return PCFieldSplitSetSchurPre(pc, ptype, pre);
2463: } /* Deprecated name */
2465: /*@
2466: PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2467: preconditioned. See `PCFieldSplitSetSchurPre()` for details.
2469: Logically Collective
2471: Input Parameter:
2472: . pc - the preconditioner context
2474: Output Parameters:
2475: + ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`
2476: - pre - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`
2478: Level: intermediate
2480: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2482: @*/
2483: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2484: {
2485: PetscFunctionBegin;
2487: PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2488: PetscFunctionReturn(PETSC_SUCCESS);
2489: }
2491: /*@
2492: PCFieldSplitSchurGetS - extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately
2494: Not Collective
2496: Input Parameter:
2497: . pc - the preconditioner context
2499: Output Parameter:
2500: . S - the Schur complement matrix
2502: Level: advanced
2504: Note:
2505: This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.
2507: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2508: `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2509: @*/
2510: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2511: {
2512: const char *t;
2513: PetscBool isfs;
2514: PC_FieldSplit *jac;
2516: PetscFunctionBegin;
2518: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2519: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2520: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2521: jac = (PC_FieldSplit *)pc->data;
2522: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2523: if (S) *S = jac->schur;
2524: PetscFunctionReturn(PETSC_SUCCESS);
2525: }
2527: /*@
2528: PCFieldSplitSchurRestoreS - returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`
2530: Not Collective
2532: Input Parameters:
2533: + pc - the preconditioner context
2534: - S - the Schur complement matrix
2536: Level: advanced
2538: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2539: @*/
2540: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2541: {
2542: const char *t;
2543: PetscBool isfs;
2544: PC_FieldSplit *jac;
2546: PetscFunctionBegin;
2548: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2549: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2550: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2551: jac = (PC_FieldSplit *)pc->data;
2552: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2553: PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2554: PetscFunctionReturn(PETSC_SUCCESS);
2555: }
2557: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2558: {
2559: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2561: PetscFunctionBegin;
2562: jac->schurpre = ptype;
2563: if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2564: PetscCall(MatDestroy(&jac->schur_user));
2565: jac->schur_user = pre;
2566: PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2567: }
2568: PetscFunctionReturn(PETSC_SUCCESS);
2569: }
2571: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2572: {
2573: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2575: PetscFunctionBegin;
2576: if (ptype) *ptype = jac->schurpre;
2577: if (pre) *pre = jac->schur_user;
2578: PetscFunctionReturn(PETSC_SUCCESS);
2579: }
2581: /*@
2582: PCFieldSplitSetSchurFactType - sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`
2584: Collective
2586: Input Parameters:
2587: + pc - the preconditioner context
2588: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default
2590: Options Database Key:
2591: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`
2593: Level: intermediate
2595: Notes:
2596: The FULL factorization is
2597: .vb
2598: (A B) = (1 0) (A 0) (1 Ainv*B) = L D U
2599: (C E) (C*Ainv 1) (0 S) (0 1)
2600: .vb
2601: where S = E - C*Ainv*B. In practice, the full factorization is applied via block triangular solves with the grouping $L*(D*U)$. UPPER uses $D*U$, LOWER uses $L*D$,
2602: and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations,
2603: thus allowing the use of `KSPMINRES)`. Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.
2605: If A and S are solved exactly
2606: .vb
2607: *) FULL factorization is a direct solver.
2608: *) The preconditioned operator with LOWER or UPPER has all eigenvalues equal to 1 and minimal polynomial of degree 2, so `KSPGMRES` converges in 2 iterations.
2609: *) With DIAG, the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so `KSPGMRES` converges in at most 4 iterations.
2610: .ve
2612: If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2613: application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.
2615: For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.
2617: A flexible method like `KSPFGMRES` or `KSPGCR`, [](sec_flexibleksp), must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used to solve with A or S).
2619: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2620: [](sec_flexibleksp)
2621: @*/
2622: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2623: {
2624: PetscFunctionBegin;
2626: PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2627: PetscFunctionReturn(PETSC_SUCCESS);
2628: }
2630: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2631: {
2632: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2634: PetscFunctionBegin;
2635: jac->schurfactorization = ftype;
2636: PetscFunctionReturn(PETSC_SUCCESS);
2637: }
2639: /*@
2640: PCFieldSplitSetSchurScale - Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.
2642: Collective
2644: Input Parameters:
2645: + pc - the preconditioner context
2646: - scale - scaling factor for the Schur complement
2648: Options Database Key:
2649: . -pc_fieldsplit_schur_scale <scale> - default is -1.0
2651: Level: intermediate
2653: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2654: @*/
2655: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2656: {
2657: PetscFunctionBegin;
2660: PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2661: PetscFunctionReturn(PETSC_SUCCESS);
2662: }
2664: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2665: {
2666: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2668: PetscFunctionBegin;
2669: jac->schurscale = scale;
2670: PetscFunctionReturn(PETSC_SUCCESS);
2671: }
2673: /*@C
2674: PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
2676: Collective
2678: Input Parameter:
2679: . pc - the preconditioner context
2681: Output Parameters:
2682: + A00 - the (0,0) block
2683: . A01 - the (0,1) block
2684: . A10 - the (1,0) block
2685: - A11 - the (1,1) block
2687: Level: advanced
2689: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2690: @*/
2691: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2692: {
2693: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2695: PetscFunctionBegin;
2697: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2698: if (A00) *A00 = jac->pmat[0];
2699: if (A01) *A01 = jac->B;
2700: if (A10) *A10 = jac->C;
2701: if (A11) *A11 = jac->pmat[1];
2702: PetscFunctionReturn(PETSC_SUCCESS);
2703: }
2705: /*@
2706: PCFieldSplitSetGKBTol - Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2708: Collective
2710: Input Parameters:
2711: + pc - the preconditioner context
2712: - tolerance - the solver tolerance
2714: Options Database Key:
2715: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5
2717: Level: intermediate
2719: Note:
2720: The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2721: It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2722: this estimate, the stopping criterion is satisfactory in practical cases.
2724: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2725: @*/
2726: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2727: {
2728: PetscFunctionBegin;
2731: PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2732: PetscFunctionReturn(PETSC_SUCCESS);
2733: }
2735: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2736: {
2737: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2739: PetscFunctionBegin;
2740: jac->gkbtol = tolerance;
2741: PetscFunctionReturn(PETSC_SUCCESS);
2742: }
2744: /*@
2745: PCFieldSplitSetGKBMaxit - Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`
2747: Collective
2749: Input Parameters:
2750: + pc - the preconditioner context
2751: - maxit - the maximum number of iterations
2753: Options Database Key:
2754: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100
2756: Level: intermediate
2758: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2759: @*/
2760: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2761: {
2762: PetscFunctionBegin;
2765: PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2766: PetscFunctionReturn(PETSC_SUCCESS);
2767: }
2769: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2770: {
2771: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2773: PetscFunctionBegin;
2774: jac->gkbmaxit = maxit;
2775: PetscFunctionReturn(PETSC_SUCCESS);
2776: }
2778: /*@
2779: PCFieldSplitSetGKBDelay - Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2780: preconditioner.
2782: Collective
2784: Input Parameters:
2785: + pc - the preconditioner context
2786: - delay - the delay window in the lower bound estimate
2788: Options Database Key:
2789: . -pc_fieldsplit_gkb_delay <delay> - default is 5
2791: Level: intermediate
2793: Notes:
2794: The algorithm uses a lower bound estimate of the error in energy norm as stopping criterion. The lower bound of the error $ ||u-u^k||_H $
2795: is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2796: at least (`delay` + 1) iterations to stop.
2798: For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`
2800: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2801: @*/
2802: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2803: {
2804: PetscFunctionBegin;
2807: PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2808: PetscFunctionReturn(PETSC_SUCCESS);
2809: }
2811: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2812: {
2813: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2815: PetscFunctionBegin;
2816: jac->gkbdelay = delay;
2817: PetscFunctionReturn(PETSC_SUCCESS);
2818: }
2820: /*@
2821: PCFieldSplitSetGKBNu - Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2822: Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2824: Collective
2826: Input Parameters:
2827: + pc - the preconditioner context
2828: - nu - the shift parameter
2830: Options Database Key:
2831: . -pc_fieldsplit_gkb_nu <nu> - default is 1
2833: Level: intermediate
2835: Notes:
2836: This shift is in general done to obtain better convergence properties for the outer loop of the algorithm. This is often achieved by choosing `nu` sufficiently large. However,
2837: if `nu` is chosen too large, the matrix H might be badly conditioned and the solution of the linear system $Hx = b$ in the inner loop becomes difficult. It is therefore
2838: necessary to find a good balance in between the convergence of the inner and outer loop.
2840: For `nu` = 0, no shift is done. In this case A00 has to be positive definite. The matrix N in {cite}`arioli2013` is then chosen as identity.
2842: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2843: @*/
2844: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2845: {
2846: PetscFunctionBegin;
2849: PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2850: PetscFunctionReturn(PETSC_SUCCESS);
2851: }
2853: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2854: {
2855: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2857: PetscFunctionBegin;
2858: jac->gkbnu = nu;
2859: PetscFunctionReturn(PETSC_SUCCESS);
2860: }
2862: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2863: {
2864: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2866: PetscFunctionBegin;
2867: jac->type = type;
2868: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2869: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2870: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2871: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2872: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2873: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2874: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2875: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2876: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2878: if (type == PC_COMPOSITE_SCHUR) {
2879: pc->ops->apply = PCApply_FieldSplit_Schur;
2880: pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2881: pc->ops->view = PCView_FieldSplit_Schur;
2883: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2884: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2885: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2886: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2887: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2888: } else if (type == PC_COMPOSITE_GKB) {
2889: pc->ops->apply = PCApply_FieldSplit_GKB;
2890: pc->ops->view = PCView_FieldSplit_GKB;
2892: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2893: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2894: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2895: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2896: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2897: } else {
2898: pc->ops->apply = PCApply_FieldSplit;
2899: pc->ops->view = PCView_FieldSplit;
2901: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2902: }
2903: PetscFunctionReturn(PETSC_SUCCESS);
2904: }
2906: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2907: {
2908: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2910: PetscFunctionBegin;
2911: PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2912: PetscCheck(jac->bs <= 0 || jac->bs == bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Cannot change fieldsplit blocksize from %" PetscInt_FMT " to %" PetscInt_FMT " after it has been set", jac->bs, bs);
2913: jac->bs = bs;
2914: PetscFunctionReturn(PETSC_SUCCESS);
2915: }
2917: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2918: {
2919: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2920: PC_FieldSplitLink ilink_current = jac->head;
2921: IS is_owned;
2923: PetscFunctionBegin;
2924: jac->coordinates_set = PETSC_TRUE; // Internal flag
2925: PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));
2927: while (ilink_current) {
2928: // For each IS, embed it to get local coords indces
2929: IS is_coords;
2930: PetscInt ndofs_block;
2931: const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block
2933: // Setting drop to true for safety. It should make no difference.
2934: PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2935: PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2936: PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));
2938: // Allocate coordinates vector and set it directly
2939: PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
2940: for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2941: for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2942: }
2943: ilink_current->dim = dim;
2944: ilink_current->ndofs = ndofs_block;
2945: PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2946: PetscCall(ISDestroy(&is_coords));
2947: ilink_current = ilink_current->next;
2948: }
2949: PetscCall(ISDestroy(&is_owned));
2950: PetscFunctionReturn(PETSC_SUCCESS);
2951: }
2953: /*@
2954: PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2956: Collective
2958: Input Parameters:
2959: + pc - the preconditioner context
2960: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2962: Options Database Key:
2963: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
2965: Level: intermediate
2967: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2968: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2969: @*/
2970: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2971: {
2972: PetscFunctionBegin;
2974: PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2975: PetscFunctionReturn(PETSC_SUCCESS);
2976: }
2978: /*@
2979: PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2981: Not collective
2983: Input Parameter:
2984: . pc - the preconditioner context
2986: Output Parameter:
2987: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2989: Level: intermediate
2991: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2992: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2993: @*/
2994: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2995: {
2996: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2998: PetscFunctionBegin;
3000: PetscAssertPointer(type, 2);
3001: *type = jac->type;
3002: PetscFunctionReturn(PETSC_SUCCESS);
3003: }
3005: /*@
3006: PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3008: Logically Collective
3010: Input Parameters:
3011: + pc - the preconditioner context
3012: - flg - boolean indicating whether to use field splits defined by the `DM`
3014: Options Database Key:
3015: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`
3017: Level: intermediate
3019: Developer Note:
3020: The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database
3022: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3023: @*/
3024: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3025: {
3026: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3027: PetscBool isfs;
3029: PetscFunctionBegin;
3032: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3033: if (isfs) jac->dm_splits = flg;
3034: PetscFunctionReturn(PETSC_SUCCESS);
3035: }
3037: /*@
3038: PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3040: Logically Collective
3042: Input Parameter:
3043: . pc - the preconditioner context
3045: Output Parameter:
3046: . flg - boolean indicating whether to use field splits defined by the `DM`
3048: Level: intermediate
3050: Developer Note:
3051: The name should be `PCFieldSplitGetUseDMSplits()`
3053: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3054: @*/
3055: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3056: {
3057: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3058: PetscBool isfs;
3060: PetscFunctionBegin;
3062: PetscAssertPointer(flg, 2);
3063: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3064: if (isfs) {
3065: if (flg) *flg = jac->dm_splits;
3066: }
3067: PetscFunctionReturn(PETSC_SUCCESS);
3068: }
3070: /*@
3071: PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3073: Logically Collective
3075: Input Parameter:
3076: . pc - the preconditioner context
3078: Output Parameter:
3079: . flg - boolean indicating whether to detect fields or not
3081: Level: intermediate
3083: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3084: @*/
3085: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3086: {
3087: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3089: PetscFunctionBegin;
3090: *flg = jac->detect;
3091: PetscFunctionReturn(PETSC_SUCCESS);
3092: }
3094: /*@
3095: PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3097: Logically Collective
3099: Input Parameter:
3100: . pc - the preconditioner context
3102: Output Parameter:
3103: . flg - boolean indicating whether to detect fields or not
3105: Options Database Key:
3106: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point
3108: Level: intermediate
3110: Note:
3111: Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).
3113: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3114: @*/
3115: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3116: {
3117: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3119: PetscFunctionBegin;
3120: jac->detect = flg;
3121: if (jac->detect) {
3122: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3123: PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3124: }
3125: PetscFunctionReturn(PETSC_SUCCESS);
3126: }
3128: /*MC
3129: PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3130: collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.
3132: Options Database Keys:
3133: + -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split
3134: . -pc_fieldsplit_default - automatically add any fields to additional splits that have not
3135: been supplied explicitly by `-pc_fieldsplit_%d_fields`
3136: . -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
3137: . -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3138: . -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()`
3139: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`;
3140: see `PCFieldSplitSetSchurFactType()`
3141: . -pc_fieldsplit_dm_splits <true,false> (default is true) - Whether to use `DMCreateFieldDecomposition()` for splits
3142: - -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver
3144: Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3145: The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3146: For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.
3148: To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3149: options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`
3151: To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3152: and set the options directly on the resulting `KSP` object
3154: Level: intermediate
3156: Notes:
3157: Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3158: to define a split by an arbitrary collection of entries.
3160: If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3161: `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise, the splits are defined by entries strided by bs,
3162: beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3163: if this is not called the block size defaults to the blocksize of the second matrix passed
3164: to `KSPSetOperators()`/`PCSetOperators()`.
3166: For the Schur complement preconditioner if
3168: ```{math}
3169: J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3170: ```
3172: the preconditioner using `full` factorization is logically
3173: ```{math}
3174: \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
3175: ```
3176: where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`. $S$ is the Schur complement
3177: ```{math}
3178: S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3179: ```
3180: which is usually dense and not stored explicitly. The action of $\text{ksp}(S)$ is computed using the KSP solver with prefix `-fieldsplit_splitname_` (where `splitname` was given
3181: in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3182: it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3183: $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.
3185: The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3186: `diag` gives
3187: ```{math}
3188: \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & -\text{ksp}(S) \end{array}\right]
3189: ```
3190: Note that, slightly counter intuitively, there is a negative in front of the $\text{ksp}(S)$ so that the preconditioner is positive definite. For SPD matrices $J$, the sign flip
3191: can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3192: ```{math}
3193: \left[\begin{array}{cc} A_{00} & 0 \\ A_{10} & S \end{array}\right]
3194: ```
3195: where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3196: ```{math}
3197: \left[\begin{array}{cc} A_{00} & A_{01} \\ 0 & S \end{array}\right]
3198: ```
3199: where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.
3201: If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3202: is used automatically for a second block.
3204: The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3205: Generally it should be used with the `MATAIJ` format.
3207: The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3208: for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3209: One can also use `PCFIELDSPLIT`
3210: inside a smoother resulting in "Distributive Smoothers".
3212: See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.
3214: The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3215: residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.
3217: The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3218: ```{math}
3219: \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3220: ```
3221: with $A_{00}$ positive semi-definite. The implementation follows {cite}`arioli2013`. Therein, we choose $N := 1/\nu * I$ and the $(1,1)$-block of the matrix is modified to $H = _{A00} + \nu*A_{01}*A_{01}'$.
3222: A linear system $Hx = b$ has to be solved in each iteration of the GKB algorithm. This solver is chosen with the option prefix `-fieldsplit_0_`.
3224: Developer Note:
3225: The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3226: user API.
3228: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3229: `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3230: `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3231: `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3232: M*/
3234: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3235: {
3236: PC_FieldSplit *jac;
3238: PetscFunctionBegin;
3239: PetscCall(PetscNew(&jac));
3241: jac->bs = -1;
3242: jac->nsplits = 0;
3243: jac->type = PC_COMPOSITE_MULTIPLICATIVE;
3244: jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3245: jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3246: jac->schurscale = -1.0;
3247: jac->dm_splits = PETSC_TRUE;
3248: jac->detect = PETSC_FALSE;
3249: jac->gkbtol = 1e-5;
3250: jac->gkbdelay = 5;
3251: jac->gkbnu = 1;
3252: jac->gkbmaxit = 100;
3253: jac->gkbmonitor = PETSC_FALSE;
3254: jac->coordinates_set = PETSC_FALSE;
3256: pc->data = (void *)jac;
3258: pc->ops->apply = PCApply_FieldSplit;
3259: pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3260: pc->ops->setup = PCSetUp_FieldSplit;
3261: pc->ops->reset = PCReset_FieldSplit;
3262: pc->ops->destroy = PCDestroy_FieldSplit;
3263: pc->ops->setfromoptions = PCSetFromOptions_FieldSplit;
3264: pc->ops->view = PCView_FieldSplit;
3265: pc->ops->applyrichardson = NULL;
3267: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3268: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3269: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3270: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3271: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3272: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3273: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3274: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3275: PetscFunctionReturn(PETSC_SUCCESS);
3276: }