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 *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(KSPGetOptionsPrefix(ilink->ksp, &prefix));
670: PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
671: PetscCall(MatSetFromOptions(jac->pmat[i]));
672: PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
673: }
674: /* create work vectors for each split */
675: PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
676: ilink->x = jac->x[i];
677: ilink->y = jac->y[i];
678: ilink->z = NULL;
679: /* compute scatter contexts needed by multiplicative versions and non-default splits */
680: PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
681: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
682: if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
683: ilink = ilink->next;
684: }
685: PetscCall(VecDestroy(&xtmp));
686: } else {
687: MatReuse scall;
688: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
689: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
690: scall = MAT_INITIAL_MATRIX;
691: } else scall = MAT_REUSE_MATRIX;
693: for (i = 0; i < nsplit; i++) {
694: Mat pmat;
696: /* Check for preconditioning matrix attached to IS */
697: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
698: if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
699: ilink = ilink->next;
700: }
701: }
702: if (jac->diag_use_amat) {
703: ilink = jac->head;
704: if (!jac->mat) {
705: PetscCall(PetscMalloc1(nsplit, &jac->mat));
706: for (i = 0; i < nsplit; i++) {
707: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
708: ilink = ilink->next;
709: }
710: } else {
711: MatReuse scall;
712: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
713: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
714: scall = MAT_INITIAL_MATRIX;
715: } else scall = MAT_REUSE_MATRIX;
717: for (i = 0; i < nsplit; i++) {
718: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
719: ilink = ilink->next;
720: }
721: }
722: } else {
723: jac->mat = jac->pmat;
724: }
726: /* Check for null space attached to IS */
727: ilink = jac->head;
728: for (i = 0; i < nsplit; i++) {
729: MatNullSpace sp;
731: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
732: if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
733: ilink = ilink->next;
734: }
736: if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
737: /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
738: /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
739: ilink = jac->head;
740: if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
741: /* 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 */
742: if (!jac->Afield) {
743: PetscCall(PetscCalloc1(nsplit, &jac->Afield));
744: if (jac->offdiag_use_amat) {
745: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
746: } else {
747: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
748: }
749: } else {
750: MatReuse scall;
752: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
753: PetscCall(MatDestroy(&jac->Afield[1]));
754: scall = MAT_INITIAL_MATRIX;
755: } else scall = MAT_REUSE_MATRIX;
757: if (jac->offdiag_use_amat) {
758: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
759: } else {
760: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
761: }
762: }
763: } else {
764: if (!jac->Afield) {
765: PetscCall(PetscMalloc1(nsplit, &jac->Afield));
766: for (i = 0; i < nsplit; i++) {
767: if (jac->offdiag_use_amat) {
768: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
769: } else {
770: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
771: }
772: ilink = ilink->next;
773: }
774: } else {
775: MatReuse scall;
776: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
777: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
778: scall = MAT_INITIAL_MATRIX;
779: } else scall = MAT_REUSE_MATRIX;
781: for (i = 0; i < nsplit; i++) {
782: if (jac->offdiag_use_amat) {
783: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
784: } else {
785: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
786: }
787: ilink = ilink->next;
788: }
789: }
790: }
791: }
793: if (jac->type == PC_COMPOSITE_SCHUR) {
794: IS ccis;
795: PetscBool isset, isspd;
796: PetscInt rstart, rend;
797: char lscname[256];
798: PetscObject LSC_L;
799: PetscBool set, flg;
801: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields");
803: /* If pc->mat is SPD, don't scale by -1 the Schur complement */
804: if (jac->schurscale == (PetscScalar)-1.0) {
805: PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
806: jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
807: }
809: /* When extracting off-diagonal submatrices, we take complements from this range */
810: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
811: PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
813: if (jac->schur) {
814: KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
815: MatReuse scall;
817: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
818: scall = MAT_INITIAL_MATRIX;
819: PetscCall(MatDestroy(&jac->B));
820: PetscCall(MatDestroy(&jac->C));
821: } else scall = MAT_REUSE_MATRIX;
823: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
824: ilink = jac->head;
825: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
826: if (jac->offdiag_use_amat) {
827: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
828: } else {
829: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
830: }
831: PetscCall(ISDestroy(&ccis));
832: if (!flg) {
833: ilink = ilink->next;
834: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
835: if (jac->offdiag_use_amat) {
836: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
837: } else {
838: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
839: }
840: PetscCall(ISDestroy(&ccis));
841: } else {
842: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
843: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
844: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
845: }
846: PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
847: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
848: PetscCall(MatDestroy(&jac->schurp));
849: PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
850: }
851: if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
852: if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
853: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
854: } else {
855: const char *Dprefix;
856: char schurprefix[256], schurmatprefix[256];
857: char schurtestoption[256];
858: MatNullSpace sp;
859: KSP kspt;
861: /* extract the A01 and A10 matrices */
862: ilink = jac->head;
863: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
864: if (jac->offdiag_use_amat) {
865: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
866: } else {
867: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
868: }
869: PetscCall(ISDestroy(&ccis));
870: ilink = ilink->next;
871: if (!flg) {
872: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
873: if (jac->offdiag_use_amat) {
874: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
875: } else {
876: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
877: }
878: PetscCall(ISDestroy(&ccis));
879: } else {
880: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
881: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
882: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
883: }
884: /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
885: PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
886: PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
887: PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
888: PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
889: PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
890: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
891: PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));
893: /* Note: this is not true in general */
894: PetscCall(MatGetNullSpace(jac->mat[1], &sp));
895: if (sp) PetscCall(MatSetNullSpace(jac->schur, sp));
897: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
898: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
899: if (flg) {
900: DM dmInner;
901: KSP kspInner;
902: PC pcInner;
904: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
905: PetscCall(KSPReset(kspInner));
906: PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
907: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
908: /* Indent this deeper to emphasize the "inner" nature of this solver. */
909: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
910: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
911: PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));
913: /* Set DM for new solver */
914: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
915: PetscCall(KSPSetDM(kspInner, dmInner));
916: PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));
918: /* Defaults to PCKSP as preconditioner */
919: PetscCall(KSPGetPC(kspInner, &pcInner));
920: PetscCall(PCSetType(pcInner, PCKSP));
921: PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
922: } else {
923: /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
924: * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
925: * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
926: * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
927: * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
928: * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
929: PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
930: PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
931: }
932: PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
933: PetscCall(KSPSetFromOptions(jac->head->ksp));
934: PetscCall(MatSetFromOptions(jac->schur));
936: PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg));
937: if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */
938: KSP kspInner;
939: PC pcInner;
941: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
942: PetscCall(KSPGetPC(kspInner, &pcInner));
943: PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
944: if (flg) {
945: KSP ksp;
947: PetscCall(PCKSPGetKSP(pcInner, &ksp));
948: if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
949: }
950: }
951: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
952: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
953: if (flg) {
954: DM dmInner;
956: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
957: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
958: PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
959: PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
960: PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
961: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
962: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
963: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
964: PetscCall(KSPSetDM(jac->kspupper, dmInner));
965: PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
966: PetscCall(KSPSetFromOptions(jac->kspupper));
967: PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
968: PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
969: } else {
970: jac->kspupper = jac->head->ksp;
971: PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
972: }
974: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
975: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
976: PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
977: PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
978: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
979: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
980: PC pcschur;
981: PetscCall(KSPGetPC(jac->kspschur, &pcschur));
982: PetscCall(PCSetType(pcschur, PCNONE));
983: /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
984: } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
985: PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
986: }
987: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
988: PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
989: PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
990: /* propagate DM */
991: {
992: DM sdm;
993: PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
994: if (sdm) {
995: PetscCall(KSPSetDM(jac->kspschur, sdm));
996: PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
997: }
998: }
999: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1000: /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1001: PetscCall(KSPSetFromOptions(jac->kspschur));
1002: }
1003: PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1004: PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1006: /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1007: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1008: PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1009: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1010: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1011: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1012: PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1013: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1014: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1015: } else if (jac->type == PC_COMPOSITE_GKB) {
1016: IS ccis;
1017: PetscInt rstart, rend;
1019: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1021: ilink = jac->head;
1023: /* When extracting off-diagonal submatrices, we take complements from this range */
1024: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
1026: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1027: if (jac->offdiag_use_amat) {
1028: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1029: } else {
1030: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1031: }
1032: PetscCall(ISDestroy(&ccis));
1033: /* Create work vectors for GKB algorithm */
1034: PetscCall(VecDuplicate(ilink->x, &jac->u));
1035: PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1036: PetscCall(VecDuplicate(ilink->x, &jac->w2));
1037: ilink = ilink->next;
1038: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1039: if (jac->offdiag_use_amat) {
1040: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1041: } else {
1042: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1043: }
1044: PetscCall(ISDestroy(&ccis));
1045: /* Create work vectors for GKB algorithm */
1046: PetscCall(VecDuplicate(ilink->x, &jac->v));
1047: PetscCall(VecDuplicate(ilink->x, &jac->d));
1048: PetscCall(VecDuplicate(ilink->x, &jac->w1));
1049: PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1050: PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));
1052: ilink = jac->head;
1053: PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1054: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1055: /* Create gkb_monitor context */
1056: if (jac->gkbmonitor) {
1057: PetscInt tablevel;
1058: PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1059: PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1060: PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1061: PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1062: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1063: }
1064: } else {
1065: /* set up the individual splits' PCs */
1066: i = 0;
1067: ilink = jac->head;
1068: while (ilink) {
1069: PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1070: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1071: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1072: i++;
1073: ilink = ilink->next;
1074: }
1075: }
1077: /* Set coordinates to the sub PC objects whenever these are set */
1078: if (jac->coordinates_set) {
1079: PC pc_coords;
1080: if (jac->type == PC_COMPOSITE_SCHUR) {
1081: // Head is first block.
1082: PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1083: PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1084: // Second one is Schur block, but its KSP object is in kspschur.
1085: PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1086: PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1087: } else if (jac->type == PC_COMPOSITE_GKB) {
1088: PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1089: } else {
1090: ilink = jac->head;
1091: while (ilink) {
1092: PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1093: PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1094: ilink = ilink->next;
1095: }
1096: }
1097: }
1099: jac->suboptionsset = PETSC_TRUE;
1100: PetscFunctionReturn(PETSC_SUCCESS);
1101: }
1103: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1104: ((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) || \
1105: 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) || \
1106: VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))
1108: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1109: {
1110: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1111: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1112: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1114: PetscFunctionBegin;
1115: switch (jac->schurfactorization) {
1116: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1117: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1118: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1119: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1120: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1121: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1122: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1123: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1124: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1125: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1126: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1127: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1128: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1129: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1130: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1131: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1132: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1133: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1134: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1135: break;
1136: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1137: /* [A00 0; A10 S], suitable for left preconditioning */
1138: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1139: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1140: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1141: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1142: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1143: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1144: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1145: PetscCall(VecScale(ilinkD->x, -1.));
1146: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1147: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1148: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1149: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1150: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1151: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1152: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1153: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1154: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1155: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1156: break;
1157: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1158: /* [A00 A01; 0 S], suitable for right preconditioning */
1159: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1160: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1161: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1162: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1163: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1164: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1165: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1166: PetscCall(VecScale(ilinkA->x, -1.));
1167: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1168: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1169: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1170: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1171: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1172: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1173: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1174: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1175: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1176: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1177: break;
1178: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1179: /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1180: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1181: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1182: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1183: PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1184: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1185: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1186: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1187: PetscCall(VecScale(ilinkD->x, -1.0));
1188: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1189: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1191: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1192: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1193: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1194: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1195: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1197: if (kspUpper == kspA) {
1198: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1199: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1200: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1201: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1202: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1203: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1204: } else {
1205: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1206: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1207: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1208: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1209: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1210: PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1211: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1212: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1213: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1214: }
1215: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1216: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1217: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1218: }
1219: PetscFunctionReturn(PETSC_SUCCESS);
1220: }
1222: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1223: {
1224: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1225: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1226: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1228: PetscFunctionBegin;
1229: switch (jac->schurfactorization) {
1230: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1231: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1232: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1233: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1234: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1235: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1236: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1237: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1238: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1239: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1240: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1241: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1242: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1243: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1244: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1245: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1246: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1247: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1248: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1249: break;
1250: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1251: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1252: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1253: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1254: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1255: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1256: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1257: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1258: PetscCall(VecScale(ilinkD->x, -1.));
1259: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1260: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1261: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1262: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1263: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1264: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1265: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1266: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1267: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1268: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1269: break;
1270: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1271: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1272: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_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(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1278: PetscCall(VecScale(ilinkA->x, -1.));
1279: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1280: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1281: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1282: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1283: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1284: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1285: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1286: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1287: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1288: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1289: break;
1290: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1291: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1292: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1293: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1294: PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1295: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1296: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1297: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1298: PetscCall(VecScale(ilinkD->x, -1.0));
1299: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1300: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1302: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1303: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1304: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1305: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1306: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1308: if (kspLower == kspA) {
1309: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1310: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1311: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1312: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1313: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1314: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1315: } else {
1316: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1317: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1318: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1319: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1320: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1321: PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1322: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1323: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1324: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1325: }
1326: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1327: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1328: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1329: }
1330: PetscFunctionReturn(PETSC_SUCCESS);
1331: }
1333: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1334: {
1335: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1336: PC_FieldSplitLink ilink = jac->head;
1337: PetscInt cnt, bs;
1339: PetscFunctionBegin;
1340: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1341: if (jac->defaultsplit) {
1342: PetscCall(VecGetBlockSize(x, &bs));
1343: 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);
1344: PetscCall(VecGetBlockSize(y, &bs));
1345: 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);
1346: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1347: while (ilink) {
1348: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1349: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1350: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1351: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1352: ilink = ilink->next;
1353: }
1354: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1355: } else {
1356: PetscCall(VecSet(y, 0.0));
1357: while (ilink) {
1358: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1359: ilink = ilink->next;
1360: }
1361: }
1362: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1363: PetscCall(VecSet(y, 0.0));
1364: /* solve on first block for first block variables */
1365: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1366: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1367: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1368: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1369: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1370: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1371: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1372: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1374: /* compute the residual only onto second block variables using first block variables */
1375: PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1376: ilink = ilink->next;
1377: PetscCall(VecScale(ilink->x, -1.0));
1378: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1379: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1381: /* solve on second block variables */
1382: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1383: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1384: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1385: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1386: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1387: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1388: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1389: if (!jac->w1) {
1390: PetscCall(VecDuplicate(x, &jac->w1));
1391: PetscCall(VecDuplicate(x, &jac->w2));
1392: }
1393: PetscCall(VecSet(y, 0.0));
1394: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1395: cnt = 1;
1396: while (ilink->next) {
1397: ilink = ilink->next;
1398: /* compute the residual only over the part of the vector needed */
1399: PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1400: PetscCall(VecScale(ilink->x, -1.0));
1401: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1402: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1403: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1404: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1405: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1406: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1407: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1408: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1409: }
1410: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1411: cnt -= 2;
1412: while (ilink->previous) {
1413: ilink = ilink->previous;
1414: /* compute the residual only over the part of the vector needed */
1415: PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1416: PetscCall(VecScale(ilink->x, -1.0));
1417: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1418: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1419: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1420: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1421: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1422: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1423: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1424: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1425: }
1426: }
1427: } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1428: PetscFunctionReturn(PETSC_SUCCESS);
1429: }
1431: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1432: {
1433: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1434: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1435: KSP ksp = ilinkA->ksp;
1436: Vec u, v, Hu, d, work1, work2;
1437: PetscScalar alpha, z, nrmz2, *vecz;
1438: PetscReal lowbnd, nu, beta;
1439: PetscInt j, iterGKB;
1441: PetscFunctionBegin;
1442: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1443: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1444: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1445: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1447: u = jac->u;
1448: v = jac->v;
1449: Hu = jac->Hu;
1450: d = jac->d;
1451: work1 = jac->w1;
1452: work2 = jac->w2;
1453: vecz = jac->vecz;
1455: /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1456: /* Add q = q + nu*B*b */
1457: if (jac->gkbnu) {
1458: nu = jac->gkbnu;
1459: PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1460: PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1461: } else {
1462: /* Situation when no augmented Lagrangian is used. Then we set inner */
1463: /* matrix N = I in [Ar13], and thus nu = 1. */
1464: nu = 1;
1465: }
1467: /* Transform rhs from [q,tilde{b}] to [0,b] */
1468: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1469: PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1470: PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1471: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1472: PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1473: PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x */
1475: /* First step of algorithm */
1476: PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1477: KSPCheckDot(ksp, beta);
1478: beta = PetscSqrtReal(nu) * beta;
1479: PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c */
1480: PetscCall(MatMult(jac->B, v, work2)); /* u = H^{-1}*B*v */
1481: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1482: PetscCall(KSPSolve(ksp, work2, u));
1483: PetscCall(KSPCheckSolve(ksp, pc, u));
1484: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1485: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1486: PetscCall(VecDot(Hu, u, &alpha));
1487: KSPCheckDot(ksp, alpha);
1488: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1489: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1490: PetscCall(VecScale(u, 1.0 / alpha));
1491: PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c */
1493: z = beta / alpha;
1494: vecz[1] = z;
1496: /* Computation of first iterate x(1) and p(1) */
1497: PetscCall(VecAXPY(ilinkA->y, z, u));
1498: PetscCall(VecCopy(d, ilinkD->y));
1499: PetscCall(VecScale(ilinkD->y, -z));
1501: iterGKB = 1;
1502: lowbnd = 2 * jac->gkbtol;
1503: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1505: while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1506: iterGKB += 1;
1507: PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1508: PetscCall(VecAXPBY(v, nu, -alpha, work1));
1509: PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v */
1510: beta = beta / PetscSqrtReal(nu);
1511: PetscCall(VecScale(v, 1.0 / beta));
1512: PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1513: PetscCall(MatMult(jac->H, u, Hu));
1514: PetscCall(VecAXPY(work2, -beta, Hu));
1515: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1516: PetscCall(KSPSolve(ksp, work2, u));
1517: PetscCall(KSPCheckSolve(ksp, pc, u));
1518: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1519: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1520: PetscCall(VecDot(Hu, u, &alpha));
1521: KSPCheckDot(ksp, alpha);
1522: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1523: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1524: PetscCall(VecScale(u, 1.0 / alpha));
1526: z = -beta / alpha * z; /* z <- beta/alpha*z */
1527: vecz[0] = z;
1529: /* Computation of new iterate x(i+1) and p(i+1) */
1530: PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1531: PetscCall(VecAXPY(ilinkA->y, z, u)); /* r = r + z*u */
1532: PetscCall(VecAXPY(ilinkD->y, -z, d)); /* p = p - z*d */
1533: PetscCall(MatMult(jac->H, ilinkA->y, Hu)); /* ||u||_H = u'*H*u */
1534: PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));
1536: /* Compute Lower Bound estimate */
1537: if (iterGKB > jac->gkbdelay) {
1538: lowbnd = 0.0;
1539: for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1540: lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1541: }
1543: for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1544: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1545: }
1547: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1548: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1549: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1550: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1552: PetscFunctionReturn(PETSC_SUCCESS);
1553: }
1555: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1556: ((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) || \
1557: 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) || \
1558: VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))
1560: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1561: {
1562: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1563: PC_FieldSplitLink ilink = jac->head;
1564: PetscInt bs;
1566: PetscFunctionBegin;
1567: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1568: if (jac->defaultsplit) {
1569: PetscCall(VecGetBlockSize(x, &bs));
1570: 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);
1571: PetscCall(VecGetBlockSize(y, &bs));
1572: 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);
1573: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1574: while (ilink) {
1575: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1576: PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1577: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1578: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1579: ilink = ilink->next;
1580: }
1581: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1582: } else {
1583: PetscCall(VecSet(y, 0.0));
1584: while (ilink) {
1585: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1586: ilink = ilink->next;
1587: }
1588: }
1589: } else {
1590: if (!jac->w1) {
1591: PetscCall(VecDuplicate(x, &jac->w1));
1592: PetscCall(VecDuplicate(x, &jac->w2));
1593: }
1594: PetscCall(VecSet(y, 0.0));
1595: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1596: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1597: while (ilink->next) {
1598: ilink = ilink->next;
1599: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1600: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1601: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1602: }
1603: while (ilink->previous) {
1604: ilink = ilink->previous;
1605: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1606: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1607: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1608: }
1609: } else {
1610: while (ilink->next) { /* get to last entry in linked list */
1611: ilink = ilink->next;
1612: }
1613: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1614: while (ilink->previous) {
1615: ilink = ilink->previous;
1616: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1617: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1618: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1619: }
1620: }
1621: }
1622: PetscFunctionReturn(PETSC_SUCCESS);
1623: }
1625: static PetscErrorCode PCReset_FieldSplit(PC pc)
1626: {
1627: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1628: PC_FieldSplitLink ilink = jac->head, next;
1630: PetscFunctionBegin;
1631: while (ilink) {
1632: PetscCall(KSPDestroy(&ilink->ksp));
1633: PetscCall(VecDestroy(&ilink->x));
1634: PetscCall(VecDestroy(&ilink->y));
1635: PetscCall(VecDestroy(&ilink->z));
1636: PetscCall(VecScatterDestroy(&ilink->sctx));
1637: PetscCall(ISDestroy(&ilink->is));
1638: PetscCall(ISDestroy(&ilink->is_col));
1639: PetscCall(PetscFree(ilink->splitname));
1640: PetscCall(PetscFree(ilink->fields));
1641: PetscCall(PetscFree(ilink->fields_col));
1642: next = ilink->next;
1643: PetscCall(PetscFree(ilink));
1644: ilink = next;
1645: }
1646: jac->head = NULL;
1647: PetscCall(PetscFree2(jac->x, jac->y));
1648: if (jac->mat && jac->mat != jac->pmat) {
1649: PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1650: } else if (jac->mat) {
1651: jac->mat = NULL;
1652: }
1653: if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1654: if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1655: jac->nsplits = 0;
1656: PetscCall(VecDestroy(&jac->w1));
1657: PetscCall(VecDestroy(&jac->w2));
1658: PetscCall(MatDestroy(&jac->schur));
1659: PetscCall(MatDestroy(&jac->schurp));
1660: PetscCall(MatDestroy(&jac->schur_user));
1661: PetscCall(KSPDestroy(&jac->kspschur));
1662: PetscCall(KSPDestroy(&jac->kspupper));
1663: PetscCall(MatDestroy(&jac->B));
1664: PetscCall(MatDestroy(&jac->C));
1665: PetscCall(MatDestroy(&jac->H));
1666: PetscCall(VecDestroy(&jac->u));
1667: PetscCall(VecDestroy(&jac->v));
1668: PetscCall(VecDestroy(&jac->Hu));
1669: PetscCall(VecDestroy(&jac->d));
1670: PetscCall(PetscFree(jac->vecz));
1671: PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1672: jac->isrestrict = PETSC_FALSE;
1673: PetscFunctionReturn(PETSC_SUCCESS);
1674: }
1676: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1677: {
1678: PetscFunctionBegin;
1679: PetscCall(PCReset_FieldSplit(pc));
1680: PetscCall(PetscFree(pc->data));
1681: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1682: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1683: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1684: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1685: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1686: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1687: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1688: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1690: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1691: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1692: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1693: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1694: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1695: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1696: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1697: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1698: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1699: PetscFunctionReturn(PETSC_SUCCESS);
1700: }
1702: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1703: {
1704: PetscInt bs;
1705: PetscBool flg;
1706: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1707: PCCompositeType ctype;
1709: PetscFunctionBegin;
1710: PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1711: PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1712: PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1713: if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1714: jac->diag_use_amat = pc->useAmat;
1715: 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));
1716: jac->offdiag_use_amat = pc->useAmat;
1717: 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));
1718: PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1719: PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1720: PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1721: if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1722: /* Only setup fields once */
1723: if ((jac->bs > 0) && (jac->nsplits == 0)) {
1724: /* only allow user to set fields from command line if bs is already known.
1725: otherwise user can set them in PCFieldSplitSetDefaults() */
1726: PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1727: if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1728: }
1729: if (jac->type == PC_COMPOSITE_SCHUR) {
1730: PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1731: if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1732: 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));
1733: PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1734: PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1735: } else if (jac->type == PC_COMPOSITE_GKB) {
1736: PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1737: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1738: PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL));
1739: PetscCheck(jac->gkbnu >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nu cannot be less than 0: value %g", (double)jac->gkbnu);
1740: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1741: PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1742: }
1743: /*
1744: In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1745: 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
1746: is called on the outer solver in case changes were made in the options database
1748: 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()
1749: 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.
1750: Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.
1752: There could be a negative side effect of calling the KSPSetFromOptions() below.
1754: If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1755: */
1756: if (jac->issetup) {
1757: PC_FieldSplitLink ilink = jac->head;
1758: if (jac->type == PC_COMPOSITE_SCHUR) {
1759: if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1760: if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1761: }
1762: while (ilink) {
1763: if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1764: ilink = ilink->next;
1765: }
1766: }
1767: PetscOptionsHeadEnd();
1768: PetscFunctionReturn(PETSC_SUCCESS);
1769: }
1771: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1772: {
1773: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1774: PC_FieldSplitLink ilink, next = jac->head;
1775: char prefix[128];
1776: PetscInt i;
1778: PetscFunctionBegin;
1779: if (jac->splitdefined) {
1780: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1781: PetscFunctionReturn(PETSC_SUCCESS);
1782: }
1783: for (i = 0; i < n; i++) {
1784: 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);
1785: PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1786: }
1787: PetscCall(PetscNew(&ilink));
1788: if (splitname) {
1789: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1790: } else {
1791: PetscCall(PetscMalloc1(3, &ilink->splitname));
1792: PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1793: }
1794: 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 */
1795: PetscCall(PetscMalloc1(n, &ilink->fields));
1796: PetscCall(PetscArraycpy(ilink->fields, fields, n));
1797: PetscCall(PetscMalloc1(n, &ilink->fields_col));
1798: PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));
1800: ilink->nfields = n;
1801: ilink->next = NULL;
1802: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1803: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1804: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1805: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1806: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1808: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1809: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1811: if (!next) {
1812: jac->head = ilink;
1813: ilink->previous = NULL;
1814: } else {
1815: while (next->next) next = next->next;
1816: next->next = ilink;
1817: ilink->previous = next;
1818: }
1819: jac->nsplits++;
1820: PetscFunctionReturn(PETSC_SUCCESS);
1821: }
1823: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1824: {
1825: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1827: PetscFunctionBegin;
1828: *subksp = NULL;
1829: if (n) *n = 0;
1830: if (jac->type == PC_COMPOSITE_SCHUR) {
1831: PetscInt nn;
1833: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1834: PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1835: nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1836: PetscCall(PetscMalloc1(nn, subksp));
1837: (*subksp)[0] = jac->head->ksp;
1838: (*subksp)[1] = jac->kspschur;
1839: if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1840: if (n) *n = nn;
1841: }
1842: PetscFunctionReturn(PETSC_SUCCESS);
1843: }
1845: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1846: {
1847: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1849: PetscFunctionBegin;
1850: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1851: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1852: PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));
1854: (*subksp)[1] = jac->kspschur;
1855: if (n) *n = jac->nsplits;
1856: PetscFunctionReturn(PETSC_SUCCESS);
1857: }
1859: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1860: {
1861: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1862: PetscInt cnt = 0;
1863: PC_FieldSplitLink ilink = jac->head;
1865: PetscFunctionBegin;
1866: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1867: while (ilink) {
1868: (*subksp)[cnt++] = ilink->ksp;
1869: ilink = ilink->next;
1870: }
1871: 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);
1872: if (n) *n = jac->nsplits;
1873: PetscFunctionReturn(PETSC_SUCCESS);
1874: }
1876: /*@C
1877: PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.
1879: Input Parameters:
1880: + pc - the preconditioner context
1881: - isy - the index set that defines the indices to which the fieldsplit is to be restricted
1883: Level: advanced
1885: Developer Notes:
1886: It seems the resulting `IS`s will not cover the entire space, so
1887: how can they define a convergent preconditioner? Needs explaining.
1889: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1890: @*/
1891: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1892: {
1893: PetscFunctionBegin;
1896: PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1897: PetscFunctionReturn(PETSC_SUCCESS);
1898: }
1900: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1901: {
1902: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1903: PC_FieldSplitLink ilink = jac->head, next;
1904: PetscInt localsize, size, sizez, i;
1905: const PetscInt *ind, *indz;
1906: PetscInt *indc, *indcz;
1907: PetscBool flg;
1909: PetscFunctionBegin;
1910: PetscCall(ISGetLocalSize(isy, &localsize));
1911: PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1912: size -= localsize;
1913: while (ilink) {
1914: IS isrl, isr;
1915: PC subpc;
1916: PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1917: PetscCall(ISGetLocalSize(isrl, &localsize));
1918: PetscCall(PetscMalloc1(localsize, &indc));
1919: PetscCall(ISGetIndices(isrl, &ind));
1920: PetscCall(PetscArraycpy(indc, ind, localsize));
1921: PetscCall(ISRestoreIndices(isrl, &ind));
1922: PetscCall(ISDestroy(&isrl));
1923: for (i = 0; i < localsize; i++) *(indc + i) += size;
1924: PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1925: PetscCall(PetscObjectReference((PetscObject)isr));
1926: PetscCall(ISDestroy(&ilink->is));
1927: ilink->is = isr;
1928: PetscCall(PetscObjectReference((PetscObject)isr));
1929: PetscCall(ISDestroy(&ilink->is_col));
1930: ilink->is_col = isr;
1931: PetscCall(ISDestroy(&isr));
1932: PetscCall(KSPGetPC(ilink->ksp, &subpc));
1933: PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1934: if (flg) {
1935: IS iszl, isz;
1936: MPI_Comm comm;
1937: PetscCall(ISGetLocalSize(ilink->is, &localsize));
1938: comm = PetscObjectComm((PetscObject)ilink->is);
1939: PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1940: PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1941: sizez -= localsize;
1942: PetscCall(ISGetLocalSize(iszl, &localsize));
1943: PetscCall(PetscMalloc1(localsize, &indcz));
1944: PetscCall(ISGetIndices(iszl, &indz));
1945: PetscCall(PetscArraycpy(indcz, indz, localsize));
1946: PetscCall(ISRestoreIndices(iszl, &indz));
1947: PetscCall(ISDestroy(&iszl));
1948: for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1949: PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1950: PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1951: PetscCall(ISDestroy(&isz));
1952: }
1953: next = ilink->next;
1954: ilink = next;
1955: }
1956: jac->isrestrict = PETSC_TRUE;
1957: PetscFunctionReturn(PETSC_SUCCESS);
1958: }
1960: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1961: {
1962: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1963: PC_FieldSplitLink ilink, next = jac->head;
1964: char prefix[128];
1966: PetscFunctionBegin;
1967: if (jac->splitdefined) {
1968: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1969: PetscFunctionReturn(PETSC_SUCCESS);
1970: }
1971: PetscCall(PetscNew(&ilink));
1972: if (splitname) {
1973: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1974: } else {
1975: PetscCall(PetscMalloc1(8, &ilink->splitname));
1976: PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1977: }
1978: 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 */
1979: PetscCall(PetscObjectReference((PetscObject)is));
1980: PetscCall(ISDestroy(&ilink->is));
1981: ilink->is = is;
1982: PetscCall(PetscObjectReference((PetscObject)is));
1983: PetscCall(ISDestroy(&ilink->is_col));
1984: ilink->is_col = is;
1985: ilink->next = NULL;
1986: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1987: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1988: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1989: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1990: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1992: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1993: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1995: if (!next) {
1996: jac->head = ilink;
1997: ilink->previous = NULL;
1998: } else {
1999: while (next->next) next = next->next;
2000: next->next = ilink;
2001: ilink->previous = next;
2002: }
2003: jac->nsplits++;
2004: PetscFunctionReturn(PETSC_SUCCESS);
2005: }
2007: /*@C
2008: PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`
2010: Logically Collective
2012: Input Parameters:
2013: + pc - the preconditioner context
2014: . splitname - name of this split, if `NULL` the number of the split is used
2015: . n - the number of fields in this split
2016: . fields - the fields in this split
2017: - 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
2018: of the matrix and fields_col provides the column indices for that block
2020: Level: intermediate
2022: Notes:
2023: Use `PCFieldSplitSetIS()` to set a general set of indices as a split.
2025: `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2026: 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
2027: 0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2028: where the numbered entries indicate what is in the split.
2030: This function is called once per split (it creates a new split each time). Solve options
2031: for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.
2033: `PCFieldSplitSetIS()` does not support having a fields_col different from fields
2035: Developer Notes:
2036: This routine does not actually create the `IS` representing the split, that is delayed
2037: until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2038: available when this routine is called.
2040: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2041: @*/
2042: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2043: {
2044: PetscFunctionBegin;
2046: PetscAssertPointer(splitname, 2);
2047: PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2048: PetscAssertPointer(fields, 4);
2049: PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2050: PetscFunctionReturn(PETSC_SUCCESS);
2051: }
2053: /*@
2054: PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2055: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.
2057: Logically Collective
2059: Input Parameters:
2060: + pc - the preconditioner object
2061: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2063: Options Database Key:
2064: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks
2066: Level: intermediate
2068: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2069: @*/
2070: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2071: {
2072: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2073: PetscBool isfs;
2075: PetscFunctionBegin;
2077: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2078: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2079: jac->diag_use_amat = flg;
2080: PetscFunctionReturn(PETSC_SUCCESS);
2081: }
2083: /*@
2084: PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2085: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.
2087: Logically Collective
2089: Input Parameter:
2090: . pc - the preconditioner object
2092: Output Parameter:
2093: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2095: Level: intermediate
2097: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2098: @*/
2099: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2100: {
2101: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2102: PetscBool isfs;
2104: PetscFunctionBegin;
2106: PetscAssertPointer(flg, 2);
2107: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2108: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2109: *flg = jac->diag_use_amat;
2110: PetscFunctionReturn(PETSC_SUCCESS);
2111: }
2113: /*@
2114: PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2115: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.
2117: Logically Collective
2119: Input Parameters:
2120: + pc - the preconditioner object
2121: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2123: Options Database Key:
2124: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks
2126: Level: intermediate
2128: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2129: @*/
2130: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2131: {
2132: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2133: PetscBool isfs;
2135: PetscFunctionBegin;
2137: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2138: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2139: jac->offdiag_use_amat = flg;
2140: PetscFunctionReturn(PETSC_SUCCESS);
2141: }
2143: /*@
2144: PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2145: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.
2147: Logically Collective
2149: Input Parameter:
2150: . pc - the preconditioner object
2152: Output Parameter:
2153: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2155: Level: intermediate
2157: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2158: @*/
2159: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2160: {
2161: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2162: PetscBool isfs;
2164: PetscFunctionBegin;
2166: PetscAssertPointer(flg, 2);
2167: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2168: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2169: *flg = jac->offdiag_use_amat;
2170: PetscFunctionReturn(PETSC_SUCCESS);
2171: }
2173: /*@C
2174: PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`
2176: Logically Collective
2178: Input Parameters:
2179: + pc - the preconditioner context
2180: . splitname - name of this split, if `NULL` the number of the split is used
2181: - is - the index set that defines the elements in this split
2183: Level: intermediate
2185: Notes:
2186: Use `PCFieldSplitSetFields()`, for splits defined by strided types.
2188: This function is called once per split (it creates a new split each time). Solve options
2189: for this split will be available under the prefix -fieldsplit_SPLITNAME_.
2191: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2192: @*/
2193: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2194: {
2195: PetscFunctionBegin;
2197: if (splitname) PetscAssertPointer(splitname, 2);
2199: PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2200: PetscFunctionReturn(PETSC_SUCCESS);
2201: }
2203: /*@C
2204: PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`
2206: Logically Collective
2208: Input Parameters:
2209: + pc - the preconditioner context
2210: - splitname - name of this split
2212: Output Parameter:
2213: . is - the index set that defines the elements in this split, or `NULL` if the split is not found
2215: Level: intermediate
2217: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2218: @*/
2219: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2220: {
2221: PetscFunctionBegin;
2223: PetscAssertPointer(splitname, 2);
2224: PetscAssertPointer(is, 3);
2225: {
2226: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2227: PC_FieldSplitLink ilink = jac->head;
2228: PetscBool found;
2230: *is = NULL;
2231: while (ilink) {
2232: PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2233: if (found) {
2234: *is = ilink->is;
2235: break;
2236: }
2237: ilink = ilink->next;
2238: }
2239: }
2240: PetscFunctionReturn(PETSC_SUCCESS);
2241: }
2243: /*@C
2244: PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`
2246: Logically Collective
2248: Input Parameters:
2249: + pc - the preconditioner context
2250: - index - index of this split
2252: Output Parameter:
2253: . is - the index set that defines the elements in this split
2255: Level: intermediate
2257: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2258: @*/
2259: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2260: {
2261: PetscFunctionBegin;
2262: PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2264: PetscAssertPointer(is, 3);
2265: {
2266: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2267: PC_FieldSplitLink ilink = jac->head;
2268: PetscInt i = 0;
2269: PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);
2271: while (i < index) {
2272: ilink = ilink->next;
2273: ++i;
2274: }
2275: PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2276: }
2277: PetscFunctionReturn(PETSC_SUCCESS);
2278: }
2280: /*@
2281: PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2282: fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.
2284: Logically Collective
2286: Input Parameters:
2287: + pc - the preconditioner context
2288: - bs - the block size
2290: Level: intermediate
2292: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2293: @*/
2294: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2295: {
2296: PetscFunctionBegin;
2299: PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2300: PetscFunctionReturn(PETSC_SUCCESS);
2301: }
2303: /*@C
2304: PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits
2306: Collective
2308: Input Parameter:
2309: . pc - the preconditioner context
2311: Output Parameters:
2312: + n - the number of splits
2313: - subksp - the array of `KSP` contexts
2315: Level: advanced
2317: Notes:
2318: After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2319: (not the `KSP`, just the array that contains them).
2321: You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.
2323: If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2324: Schur complement and the `KSP` object used to iterate over the Schur complement.
2325: To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.
2327: If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2328: inner linear system defined by the matrix H in each loop.
2330: Fortran Notes:
2331: You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2332: You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2333: `KSP` array must be.
2335: Developer Notes:
2336: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2338: The Fortran interface should be modernized to return directly the array of values.
2340: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2341: @*/
2342: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2343: {
2344: PetscFunctionBegin;
2346: if (n) PetscAssertPointer(n, 2);
2347: PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2348: PetscFunctionReturn(PETSC_SUCCESS);
2349: }
2351: /*@C
2352: PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`
2354: Collective
2356: Input Parameter:
2357: . pc - the preconditioner context
2359: Output Parameters:
2360: + n - the number of splits
2361: - subksp - the array of `KSP` contexts
2363: Level: advanced
2365: Notes:
2366: After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2367: (not the `KSP` just the array that contains them).
2369: You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.
2371: If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2372: + 1 - the `KSP` used for the (1,1) block
2373: . 2 - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2374: - 3 - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).
2376: It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.
2378: Fortran Notes:
2379: You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2380: You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2381: `KSP` array must be.
2383: Developer Notes:
2384: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2386: Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?
2388: The Fortran interface should be modernized to return directly the array of values.
2390: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2391: @*/
2392: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2393: {
2394: PetscFunctionBegin;
2396: if (n) PetscAssertPointer(n, 2);
2397: PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2398: PetscFunctionReturn(PETSC_SUCCESS);
2399: }
2401: /*@
2402: PCFieldSplitSetSchurPre - Indicates from what operator the preconditioner is constructucted for the Schur complement.
2403: The default is the A11 matrix.
2405: Collective
2407: Input Parameters:
2408: + pc - the preconditioner context
2409: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2410: `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2411: `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2412: - pre - matrix to use for preconditioning, or `NULL`
2414: Options Database Keys:
2415: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2416: - -fieldsplit_1_pc_type <pctype> - the preconditioner algorithm that is used to construct the preconditioner from the operator
2418: Level: intermediate
2420: Notes:
2421: If ptype is
2422: + a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2423: matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2424: . self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2425: The only preconditioner that currently works with this symbolic representation matrix object is the `PCLSC`
2426: preconditioner
2427: . user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2428: to this function).
2429: . selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2430: This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2431: lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2432: - full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2433: computed internally by `PCFIELDSPLIT` (this is expensive)
2434: useful mostly as a test that the Schur complement approach can work for your problem
2436: When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2437: with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2438: `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.
2440: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2441: `MatSchurComplementSetAinvType()`, `PCLSC`,
2443: @*/
2444: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2445: {
2446: PetscFunctionBegin;
2448: PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2449: PetscFunctionReturn(PETSC_SUCCESS);
2450: }
2452: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2453: {
2454: return PCFieldSplitSetSchurPre(pc, ptype, pre);
2455: } /* Deprecated name */
2457: /*@
2458: PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2459: preconditioned. See `PCFieldSplitSetSchurPre()` for details.
2461: Logically Collective
2463: Input Parameter:
2464: . pc - the preconditioner context
2466: Output Parameters:
2467: + 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`
2468: - pre - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`
2470: Level: intermediate
2472: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2474: @*/
2475: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2476: {
2477: PetscFunctionBegin;
2479: PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2480: PetscFunctionReturn(PETSC_SUCCESS);
2481: }
2483: /*@
2484: PCFieldSplitSchurGetS - extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately
2486: Not Collective
2488: Input Parameter:
2489: . pc - the preconditioner context
2491: Output Parameter:
2492: . S - the Schur complement matrix
2494: Level: advanced
2496: Note:
2497: This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.
2499: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2500: `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2501: @*/
2502: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2503: {
2504: const char *t;
2505: PetscBool isfs;
2506: PC_FieldSplit *jac;
2508: PetscFunctionBegin;
2510: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2511: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2512: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2513: jac = (PC_FieldSplit *)pc->data;
2514: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2515: if (S) *S = jac->schur;
2516: PetscFunctionReturn(PETSC_SUCCESS);
2517: }
2519: /*@
2520: PCFieldSplitSchurRestoreS - returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`
2522: Not Collective
2524: Input Parameters:
2525: + pc - the preconditioner context
2526: - S - the Schur complement matrix
2528: Level: advanced
2530: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2531: @*/
2532: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2533: {
2534: const char *t;
2535: PetscBool isfs;
2536: PC_FieldSplit *jac;
2538: PetscFunctionBegin;
2540: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2541: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2542: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2543: jac = (PC_FieldSplit *)pc->data;
2544: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2545: PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2546: PetscFunctionReturn(PETSC_SUCCESS);
2547: }
2549: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2550: {
2551: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2553: PetscFunctionBegin;
2554: jac->schurpre = ptype;
2555: if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2556: PetscCall(MatDestroy(&jac->schur_user));
2557: jac->schur_user = pre;
2558: PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2559: }
2560: PetscFunctionReturn(PETSC_SUCCESS);
2561: }
2563: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2564: {
2565: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2567: PetscFunctionBegin;
2568: if (ptype) *ptype = jac->schurpre;
2569: if (pre) *pre = jac->schur_user;
2570: PetscFunctionReturn(PETSC_SUCCESS);
2571: }
2573: /*@
2574: PCFieldSplitSetSchurFactType - sets which blocks of the approximate block factorization to retain in the preconditioner
2576: Collective
2578: Input Parameters:
2579: + pc - the preconditioner context
2580: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default
2582: Options Database Key:
2583: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`
2585: Level: intermediate
2587: Notes:
2588: The FULL factorization is
2590: .vb
2591: (A B) = (1 0) (A 0) (1 Ainv*B) = L D U
2592: (C E) (C*Ainv 1) (0 S) (0 1)
2593: .vb
2594: 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,
2595: and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations, thus allowing the use of `KSPMINRES)`.
2596: Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.
2598: If A and S are solved exactly
2599: .vb
2600: *) FULL factorization is a direct solver.
2601: *) 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.
2602: *) 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.
2603: .ve
2605: If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2606: application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.
2608: For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.
2610: A flexible method like `KSPFGMRES` or `KSPGCR` 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).
2612: References:
2613: + * - Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000).
2614: - * - Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001).
2616: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`
2617: @*/
2618: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2619: {
2620: PetscFunctionBegin;
2622: PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2623: PetscFunctionReturn(PETSC_SUCCESS);
2624: }
2626: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2627: {
2628: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2630: PetscFunctionBegin;
2631: jac->schurfactorization = ftype;
2632: PetscFunctionReturn(PETSC_SUCCESS);
2633: }
2635: /*@
2636: PCFieldSplitSetSchurScale - Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.
2638: Collective
2640: Input Parameters:
2641: + pc - the preconditioner context
2642: - scale - scaling factor for the Schur complement
2644: Options Database Key:
2645: . -pc_fieldsplit_schur_scale - default is -1.0
2647: Level: intermediate
2649: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2650: @*/
2651: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2652: {
2653: PetscFunctionBegin;
2656: PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2657: PetscFunctionReturn(PETSC_SUCCESS);
2658: }
2660: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2661: {
2662: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2664: PetscFunctionBegin;
2665: jac->schurscale = scale;
2666: PetscFunctionReturn(PETSC_SUCCESS);
2667: }
2669: /*@C
2670: PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
2672: Collective
2674: Input Parameter:
2675: . pc - the preconditioner context
2677: Output Parameters:
2678: + A00 - the (0,0) block
2679: . A01 - the (0,1) block
2680: . A10 - the (1,0) block
2681: - A11 - the (1,1) block
2683: Level: advanced
2685: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2686: @*/
2687: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2688: {
2689: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2691: PetscFunctionBegin;
2693: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2694: if (A00) *A00 = jac->pmat[0];
2695: if (A01) *A01 = jac->B;
2696: if (A10) *A10 = jac->C;
2697: if (A11) *A11 = jac->pmat[1];
2698: PetscFunctionReturn(PETSC_SUCCESS);
2699: }
2701: /*@
2702: PCFieldSplitSetGKBTol - Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`
2704: Collective
2706: Input Parameters:
2707: + pc - the preconditioner context
2708: - tolerance - the solver tolerance
2710: Options Database Key:
2711: . -pc_fieldsplit_gkb_tol - default is 1e-5
2713: Level: intermediate
2715: Note:
2716: The generalized GKB algorithm uses a lower bound estimate of the error in energy norm as stopping criterion.
2717: It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2718: this estimate, the stopping criterion is satisfactory in practical cases [A13].
2720: References:
2721: [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.
2723: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2724: @*/
2725: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2726: {
2727: PetscFunctionBegin;
2730: PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2731: PetscFunctionReturn(PETSC_SUCCESS);
2732: }
2734: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2735: {
2736: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2738: PetscFunctionBegin;
2739: jac->gkbtol = tolerance;
2740: PetscFunctionReturn(PETSC_SUCCESS);
2741: }
2743: /*@
2744: PCFieldSplitSetGKBMaxit - Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`
2746: Collective
2748: Input Parameters:
2749: + pc - the preconditioner context
2750: - maxit - the maximum number of iterations
2752: Options Database Key:
2753: . -pc_fieldsplit_gkb_maxit - default is 100
2755: Level: intermediate
2757: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2758: @*/
2759: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2760: {
2761: PetscFunctionBegin;
2764: PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2765: PetscFunctionReturn(PETSC_SUCCESS);
2766: }
2768: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2769: {
2770: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2772: PetscFunctionBegin;
2773: jac->gkbmaxit = maxit;
2774: PetscFunctionReturn(PETSC_SUCCESS);
2775: }
2777: /*@
2778: PCFieldSplitSetGKBDelay - Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization in `PCFIELDSPLIT`
2779: preconditioner.
2781: Collective
2783: Input Parameters:
2784: + pc - the preconditioner context
2785: - delay - the delay window in the lower bound estimate
2787: Options Database Key:
2788: . -pc_fieldsplit_gkb_delay - default is 5
2790: Level: intermediate
2792: Note:
2793: 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
2794: is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + delay), and thus the algorithm needs
2795: at least (delay + 1) iterations to stop. For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to
2797: References:
2798: [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.
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 Golub-Kahan bidiagonalization preconditioner
2822: 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 - 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 big. However,
2837: if nu is chosen too big, 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 [Ar13] is then chosen as identity.
2842: References:
2843: [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.
2845: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2846: @*/
2847: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2848: {
2849: PetscFunctionBegin;
2852: PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2853: PetscFunctionReturn(PETSC_SUCCESS);
2854: }
2856: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2857: {
2858: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2860: PetscFunctionBegin;
2861: jac->gkbnu = nu;
2862: PetscFunctionReturn(PETSC_SUCCESS);
2863: }
2865: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2866: {
2867: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2869: PetscFunctionBegin;
2870: jac->type = type;
2871: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2872: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2873: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2874: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2875: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2876: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2877: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2878: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2879: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2881: if (type == PC_COMPOSITE_SCHUR) {
2882: pc->ops->apply = PCApply_FieldSplit_Schur;
2883: pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2884: pc->ops->view = PCView_FieldSplit_Schur;
2886: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2887: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2888: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2889: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2890: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2891: } else if (type == PC_COMPOSITE_GKB) {
2892: pc->ops->apply = PCApply_FieldSplit_GKB;
2893: pc->ops->view = PCView_FieldSplit_GKB;
2895: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2896: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2897: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2898: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2899: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2900: } else {
2901: pc->ops->apply = PCApply_FieldSplit;
2902: pc->ops->view = PCView_FieldSplit;
2904: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2905: }
2906: PetscFunctionReturn(PETSC_SUCCESS);
2907: }
2909: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2910: {
2911: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2913: PetscFunctionBegin;
2914: PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2915: 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);
2916: jac->bs = bs;
2917: PetscFunctionReturn(PETSC_SUCCESS);
2918: }
2920: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2921: {
2922: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2923: PC_FieldSplitLink ilink_current = jac->head;
2924: IS is_owned;
2926: PetscFunctionBegin;
2927: jac->coordinates_set = PETSC_TRUE; // Internal flag
2928: PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));
2930: while (ilink_current) {
2931: // For each IS, embed it to get local coords indces
2932: IS is_coords;
2933: PetscInt ndofs_block;
2934: const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block
2936: // Setting drop to true for safety. It should make no difference.
2937: PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2938: PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2939: PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));
2941: // Allocate coordinates vector and set it directly
2942: PetscCall(PetscMalloc1(ndofs_block * dim, &(ilink_current->coords)));
2943: for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2944: for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2945: }
2946: ilink_current->dim = dim;
2947: ilink_current->ndofs = ndofs_block;
2948: PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2949: PetscCall(ISDestroy(&is_coords));
2950: ilink_current = ilink_current->next;
2951: }
2952: PetscCall(ISDestroy(&is_owned));
2953: PetscFunctionReturn(PETSC_SUCCESS);
2954: }
2956: /*@
2957: PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2959: Collective
2961: Input Parameters:
2962: + pc - the preconditioner context
2963: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2965: Options Database Key:
2966: . -pc_fieldsplit_type <type: one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
2968: Level: intermediate
2970: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2971: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2972: @*/
2973: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2974: {
2975: PetscFunctionBegin;
2977: PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2978: PetscFunctionReturn(PETSC_SUCCESS);
2979: }
2981: /*@
2982: PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2984: Not collective
2986: Input Parameter:
2987: . pc - the preconditioner context
2989: Output Parameter:
2990: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2992: Level: intermediate
2994: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2995: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2996: @*/
2997: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2998: {
2999: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3001: PetscFunctionBegin;
3003: PetscAssertPointer(type, 2);
3004: *type = jac->type;
3005: PetscFunctionReturn(PETSC_SUCCESS);
3006: }
3008: /*@
3009: PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3011: Logically Collective
3013: Input Parameters:
3014: + pc - the preconditioner context
3015: - flg - boolean indicating whether to use field splits defined by the `DM`
3017: Options Database Key:
3018: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`
3020: Level: intermediate
3022: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `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: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3051: @*/
3052: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3053: {
3054: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3055: PetscBool isfs;
3057: PetscFunctionBegin;
3059: PetscAssertPointer(flg, 2);
3060: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3061: if (isfs) {
3062: if (flg) *flg = jac->dm_splits;
3063: }
3064: PetscFunctionReturn(PETSC_SUCCESS);
3065: }
3067: /*@
3068: PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3070: Logically Collective
3072: Input Parameter:
3073: . pc - the preconditioner context
3075: Output Parameter:
3076: . flg - boolean indicating whether to detect fields or not
3078: Level: intermediate
3080: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3081: @*/
3082: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3083: {
3084: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3086: PetscFunctionBegin;
3087: *flg = jac->detect;
3088: PetscFunctionReturn(PETSC_SUCCESS);
3089: }
3091: /*@
3092: PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3094: Logically Collective
3096: Input Parameter:
3097: . pc - the preconditioner context
3099: Output Parameter:
3100: . flg - boolean indicating whether to detect fields or not
3102: Options Database Key:
3103: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point
3105: Level: intermediate
3107: Note:
3108: Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).
3110: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3111: @*/
3112: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3113: {
3114: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3116: PetscFunctionBegin;
3117: jac->detect = flg;
3118: if (jac->detect) {
3119: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3120: PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3121: }
3122: PetscFunctionReturn(PETSC_SUCCESS);
3123: }
3125: /*MC
3126: PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3127: collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.
3129: Options Database Keys:
3130: + -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split
3131: . -pc_fieldsplit_default - automatically add any fields to additional splits that have not
3132: been supplied explicitly by `-pc_fieldsplit_%d_fields`
3133: . -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
3134: . -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3135: . -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()`
3136: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`; see `PCFieldSplitSetSchurFactType()`
3137: - -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver
3139: Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3140: The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3141: For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.
3143: To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3144: options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`
3146: To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3147: and set the options directly on the resulting `KSP` object
3149: Level: intermediate
3151: Notes:
3152: Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3153: to define a split by an arbitrary collection of entries.
3155: If no splits are set the default is used. The splits are defined by entries strided by bs,
3156: beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3157: if this is not called the block size defaults to the blocksize of the second matrix passed
3158: to `KSPSetOperators()`/`PCSetOperators()`.
3160: For the Schur complement preconditioner if
3162: ```{math}
3163: J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3164: ```
3166: the preconditioner using `full` factorization is logically
3167: ```{math}
3168: \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) \\ 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]
3169: ```
3170: where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`. $S$ is the Schur complement
3171: ```{math}
3172: S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3173: ```
3174: 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
3175: in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3176: it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3177: $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.
3179: The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3180: `diag` gives
3181: ```{math}
3182: \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & -\text{ksp}(S) \end{array}\right]
3183: ```
3184: 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
3185: can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3186: ```{math}
3187: \left[\begin{array}{cc} A_{00} & 0 \\ A_{10} & S \end{array}\right]
3188: ```
3189: where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3190: ```{math}
3191: \left[\begin{array}{cc} A_{00} & A_{01} \\ 0 & S \end{array}\right]
3192: ```
3193: where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.
3195: If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3196: is used automatically for a second block.
3198: The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3199: Generally it should be used with the `MATAIJ` format.
3201: The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3202: for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3203: One can also use `PCFIELDSPLIT`
3204: inside a smoother resulting in "Distributive Smoothers".
3206: See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.
3208: The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3209: residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.
3211: The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3212: ```{math}
3213: \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3214: ```
3215: 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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3216: 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_`.
3218: Developer Note:
3219: The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3220: user API.
3222: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3223: `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3224: `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3225: `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3226: M*/
3228: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3229: {
3230: PC_FieldSplit *jac;
3232: PetscFunctionBegin;
3233: PetscCall(PetscNew(&jac));
3235: jac->bs = -1;
3236: jac->nsplits = 0;
3237: jac->type = PC_COMPOSITE_MULTIPLICATIVE;
3238: jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3239: jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3240: jac->schurscale = -1.0;
3241: jac->dm_splits = PETSC_TRUE;
3242: jac->detect = PETSC_FALSE;
3243: jac->gkbtol = 1e-5;
3244: jac->gkbdelay = 5;
3245: jac->gkbnu = 1;
3246: jac->gkbmaxit = 100;
3247: jac->gkbmonitor = PETSC_FALSE;
3248: jac->coordinates_set = PETSC_FALSE;
3250: pc->data = (void *)jac;
3252: pc->ops->apply = PCApply_FieldSplit;
3253: pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3254: pc->ops->setup = PCSetUp_FieldSplit;
3255: pc->ops->reset = PCReset_FieldSplit;
3256: pc->ops->destroy = PCDestroy_FieldSplit;
3257: pc->ops->setfromoptions = PCSetFromOptions_FieldSplit;
3258: pc->ops->view = PCView_FieldSplit;
3259: pc->ops->applyrichardson = NULL;
3261: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3262: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3263: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3264: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3265: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3266: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3267: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3268: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3269: PetscFunctionReturn(PETSC_SUCCESS);
3270: }