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(MatGetOptionsPrefix(jac->pmat[i], &prefix));
670: if (!prefix) {
671: PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
672: PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
673: }
674: PetscCall(MatSetFromOptions(jac->pmat[i]));
675: PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
676: }
677: /* create work vectors for each split */
678: PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
679: ilink->x = jac->x[i];
680: ilink->y = jac->y[i];
681: ilink->z = NULL;
682: /* compute scatter contexts needed by multiplicative versions and non-default splits */
683: PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
684: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
685: if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
686: ilink = ilink->next;
687: }
688: PetscCall(VecDestroy(&xtmp));
689: } else {
690: MatReuse scall;
691: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
692: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
693: scall = MAT_INITIAL_MATRIX;
694: } else scall = MAT_REUSE_MATRIX;
696: for (i = 0; i < nsplit; i++) {
697: Mat pmat;
699: /* Check for preconditioning matrix attached to IS */
700: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
701: if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
702: ilink = ilink->next;
703: }
704: }
705: if (jac->diag_use_amat) {
706: ilink = jac->head;
707: if (!jac->mat) {
708: PetscCall(PetscMalloc1(nsplit, &jac->mat));
709: for (i = 0; i < nsplit; i++) {
710: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
711: ilink = ilink->next;
712: }
713: } else {
714: MatReuse scall;
715: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
716: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
717: scall = MAT_INITIAL_MATRIX;
718: } else scall = MAT_REUSE_MATRIX;
720: for (i = 0; i < nsplit; i++) {
721: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
722: ilink = ilink->next;
723: }
724: }
725: } else {
726: jac->mat = jac->pmat;
727: }
729: /* Check for null space attached to IS */
730: ilink = jac->head;
731: for (i = 0; i < nsplit; i++) {
732: MatNullSpace sp;
734: PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
735: if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
736: ilink = ilink->next;
737: }
739: if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
740: /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
741: /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
742: ilink = jac->head;
743: if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
744: /* 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 */
745: if (!jac->Afield) {
746: PetscCall(PetscCalloc1(nsplit, &jac->Afield));
747: if (jac->offdiag_use_amat) {
748: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
749: } else {
750: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
751: }
752: } else {
753: MatReuse scall;
755: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
756: PetscCall(MatDestroy(&jac->Afield[1]));
757: scall = MAT_INITIAL_MATRIX;
758: } else scall = MAT_REUSE_MATRIX;
760: if (jac->offdiag_use_amat) {
761: PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
762: } else {
763: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
764: }
765: }
766: } else {
767: if (!jac->Afield) {
768: PetscCall(PetscMalloc1(nsplit, &jac->Afield));
769: for (i = 0; i < nsplit; i++) {
770: if (jac->offdiag_use_amat) {
771: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
772: } else {
773: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
774: }
775: ilink = ilink->next;
776: }
777: } else {
778: MatReuse scall;
779: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
780: for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
781: scall = MAT_INITIAL_MATRIX;
782: } else scall = MAT_REUSE_MATRIX;
784: for (i = 0; i < nsplit; i++) {
785: if (jac->offdiag_use_amat) {
786: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
787: } else {
788: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
789: }
790: ilink = ilink->next;
791: }
792: }
793: }
794: }
796: if (jac->type == PC_COMPOSITE_SCHUR) {
797: IS ccis;
798: PetscBool isset, isspd;
799: PetscInt rstart, rend;
800: char lscname[256];
801: PetscObject LSC_L;
802: PetscBool set, flg;
804: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields");
806: /* If pc->mat is SPD, don't scale by -1 the Schur complement */
807: if (jac->schurscale == (PetscScalar)-1.0) {
808: PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
809: jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
810: }
812: /* When extracting off-diagonal submatrices, we take complements from this range */
813: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
814: PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
816: if (jac->schur) {
817: KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
818: MatReuse scall;
820: if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
821: scall = MAT_INITIAL_MATRIX;
822: PetscCall(MatDestroy(&jac->B));
823: PetscCall(MatDestroy(&jac->C));
824: } else scall = MAT_REUSE_MATRIX;
826: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
827: ilink = jac->head;
828: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
829: if (jac->offdiag_use_amat) {
830: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
831: } else {
832: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
833: }
834: PetscCall(ISDestroy(&ccis));
835: if (!flg) {
836: ilink = ilink->next;
837: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
838: if (jac->offdiag_use_amat) {
839: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
840: } else {
841: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
842: }
843: PetscCall(ISDestroy(&ccis));
844: } else {
845: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
846: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
847: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
848: }
849: PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
850: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
851: PetscCall(MatDestroy(&jac->schurp));
852: PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
853: }
854: if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
855: if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
856: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
857: } else {
858: const char *Dprefix;
859: char schurprefix[256], schurmatprefix[256];
860: char schurtestoption[256];
861: MatNullSpace sp;
862: KSP kspt;
864: /* extract the A01 and A10 matrices */
865: ilink = jac->head;
866: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
867: if (jac->offdiag_use_amat) {
868: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
869: } else {
870: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
871: }
872: PetscCall(ISDestroy(&ccis));
873: ilink = ilink->next;
874: if (!flg) {
875: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
876: if (jac->offdiag_use_amat) {
877: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
878: } else {
879: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
880: }
881: PetscCall(ISDestroy(&ccis));
882: } else {
883: PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
884: if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
885: else PetscCall(MatCreateTranspose(jac->B, &jac->C));
886: }
887: /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
888: PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
889: PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
890: PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
891: PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
892: PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
893: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
894: PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));
896: /* Note: this is not true in general */
897: PetscCall(MatGetNullSpace(jac->mat[1], &sp));
898: if (sp) PetscCall(MatSetNullSpace(jac->schur, sp));
900: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
901: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
902: if (flg) {
903: DM dmInner;
904: KSP kspInner;
905: PC pcInner;
907: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
908: PetscCall(KSPReset(kspInner));
909: PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
910: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
911: /* Indent this deeper to emphasize the "inner" nature of this solver. */
912: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
913: PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
914: PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));
916: /* Set DM for new solver */
917: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
918: PetscCall(KSPSetDM(kspInner, dmInner));
919: PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));
921: /* Defaults to PCKSP as preconditioner */
922: PetscCall(KSPGetPC(kspInner, &pcInner));
923: PetscCall(PCSetType(pcInner, PCKSP));
924: PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
925: } else {
926: /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
927: * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
928: * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
929: * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
930: * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
931: * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
932: PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
933: PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
934: }
935: PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
936: PetscCall(KSPSetFromOptions(jac->head->ksp));
937: PetscCall(MatSetFromOptions(jac->schur));
939: PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg));
940: if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */
941: KSP kspInner;
942: PC pcInner;
944: PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
945: PetscCall(KSPGetPC(kspInner, &pcInner));
946: PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
947: if (flg) {
948: KSP ksp;
950: PetscCall(PCKSPGetKSP(pcInner, &ksp));
951: if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
952: }
953: }
954: PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
955: PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
956: if (flg) {
957: DM dmInner;
959: PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
960: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
961: PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
962: PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
963: PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
964: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
965: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
966: PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
967: PetscCall(KSPSetDM(jac->kspupper, dmInner));
968: PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
969: PetscCall(KSPSetFromOptions(jac->kspupper));
970: PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
971: PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
972: } else {
973: jac->kspupper = jac->head->ksp;
974: PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
975: }
977: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
978: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
979: PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
980: PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
981: PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
982: if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
983: PC pcschur;
984: PetscCall(KSPGetPC(jac->kspschur, &pcschur));
985: PetscCall(PCSetType(pcschur, PCNONE));
986: /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
987: } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
988: PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
989: }
990: PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
991: PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
992: PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
993: /* propagate DM */
994: {
995: DM sdm;
996: PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
997: if (sdm) {
998: PetscCall(KSPSetDM(jac->kspschur, sdm));
999: PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1000: }
1001: }
1002: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1003: /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1004: PetscCall(KSPSetFromOptions(jac->kspschur));
1005: }
1006: PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1007: PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1009: /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1010: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1011: PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1012: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1013: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1014: PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1015: PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1016: if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1017: if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1018: } else if (jac->type == PC_COMPOSITE_GKB) {
1019: IS ccis;
1020: PetscInt rstart, rend;
1022: PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1024: ilink = jac->head;
1026: /* When extracting off-diagonal submatrices, we take complements from this range */
1027: PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
1029: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1030: if (jac->offdiag_use_amat) {
1031: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1032: } else {
1033: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1034: }
1035: PetscCall(ISDestroy(&ccis));
1036: /* Create work vectors for GKB algorithm */
1037: PetscCall(VecDuplicate(ilink->x, &jac->u));
1038: PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1039: PetscCall(VecDuplicate(ilink->x, &jac->w2));
1040: ilink = ilink->next;
1041: PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1042: if (jac->offdiag_use_amat) {
1043: PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1044: } else {
1045: PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1046: }
1047: PetscCall(ISDestroy(&ccis));
1048: /* Create work vectors for GKB algorithm */
1049: PetscCall(VecDuplicate(ilink->x, &jac->v));
1050: PetscCall(VecDuplicate(ilink->x, &jac->d));
1051: PetscCall(VecDuplicate(ilink->x, &jac->w1));
1052: PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1053: PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));
1055: ilink = jac->head;
1056: PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1057: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1058: /* Create gkb_monitor context */
1059: if (jac->gkbmonitor) {
1060: PetscInt tablevel;
1061: PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1062: PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1063: PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1064: PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1065: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1066: }
1067: } else {
1068: /* set up the individual splits' PCs */
1069: i = 0;
1070: ilink = jac->head;
1071: while (ilink) {
1072: PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1073: /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1074: if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1075: i++;
1076: ilink = ilink->next;
1077: }
1078: }
1080: /* Set coordinates to the sub PC objects whenever these are set */
1081: if (jac->coordinates_set) {
1082: PC pc_coords;
1083: if (jac->type == PC_COMPOSITE_SCHUR) {
1084: // Head is first block.
1085: PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1086: PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1087: // Second one is Schur block, but its KSP object is in kspschur.
1088: PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1089: PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1090: } else if (jac->type == PC_COMPOSITE_GKB) {
1091: PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1092: } else {
1093: ilink = jac->head;
1094: while (ilink) {
1095: PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1096: PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1097: ilink = ilink->next;
1098: }
1099: }
1100: }
1102: jac->suboptionsset = PETSC_TRUE;
1103: PetscFunctionReturn(PETSC_SUCCESS);
1104: }
1106: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1107: ((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) || \
1108: 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) || \
1109: VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))
1111: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1112: {
1113: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1114: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1115: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1117: PetscFunctionBegin;
1118: switch (jac->schurfactorization) {
1119: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1120: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1121: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1122: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1123: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1124: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1125: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1126: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1127: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1128: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1129: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1130: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1131: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1132: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1133: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1134: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1135: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1136: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1137: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1138: break;
1139: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1140: /* [A00 0; A10 S], suitable for left preconditioning */
1141: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1142: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1143: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1144: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1145: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1146: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1147: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1148: PetscCall(VecScale(ilinkD->x, -1.));
1149: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1150: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1151: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1152: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1153: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1154: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1155: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1156: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1157: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1158: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1159: break;
1160: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1161: /* [A00 A01; 0 S], suitable for right preconditioning */
1162: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1163: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1164: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1165: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1166: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1167: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1168: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1169: PetscCall(VecScale(ilinkA->x, -1.));
1170: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1171: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1172: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1173: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1174: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1175: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1176: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1177: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1178: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1179: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1180: break;
1181: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1182: /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1183: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1184: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1185: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1186: PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1187: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1188: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1189: PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1190: PetscCall(VecScale(ilinkD->x, -1.0));
1191: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1192: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1194: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1195: PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1196: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1197: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1198: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1200: if (kspUpper == kspA) {
1201: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1202: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1203: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1204: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1205: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1206: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1207: } else {
1208: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1209: PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1210: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1211: PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1212: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1213: PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1214: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1215: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1216: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1217: }
1218: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1219: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1220: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1221: }
1222: PetscFunctionReturn(PETSC_SUCCESS);
1223: }
1225: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1226: {
1227: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1228: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1229: KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1231: PetscFunctionBegin;
1232: switch (jac->schurfactorization) {
1233: case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1234: /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1235: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1236: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1237: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1238: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1239: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1240: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1241: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1242: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1243: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1244: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1245: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1246: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1247: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1248: PetscCall(VecScale(ilinkD->y, jac->schurscale));
1249: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1250: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1252: break;
1253: case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1254: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1255: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1256: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1257: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1258: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1259: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1260: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1261: PetscCall(VecScale(ilinkD->x, -1.));
1262: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1263: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1264: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1265: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1266: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1267: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1268: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1269: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1270: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1271: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1272: break;
1273: case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1274: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1275: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1276: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1278: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1279: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1280: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1281: PetscCall(VecScale(ilinkA->x, -1.));
1282: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1283: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1284: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1285: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1286: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1287: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1288: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1289: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1290: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1291: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1292: break;
1293: case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1294: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1295: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1296: PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1297: PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1298: PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1299: PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1300: PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1301: PetscCall(VecScale(ilinkD->x, -1.0));
1302: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1303: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1305: PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1306: PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1307: PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1308: PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1309: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1311: if (kspLower == kspA) {
1312: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1313: PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1314: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1315: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1316: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1317: PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1318: } else {
1319: PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1320: PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1321: PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1322: PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1323: PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1324: PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1325: PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1326: PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1327: PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1328: }
1329: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1330: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1331: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1332: }
1333: PetscFunctionReturn(PETSC_SUCCESS);
1334: }
1336: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1337: {
1338: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1339: PC_FieldSplitLink ilink = jac->head;
1340: PetscInt cnt, bs;
1342: PetscFunctionBegin;
1343: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1344: if (jac->defaultsplit) {
1345: PetscCall(VecGetBlockSize(x, &bs));
1346: 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);
1347: PetscCall(VecGetBlockSize(y, &bs));
1348: 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);
1349: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1350: while (ilink) {
1351: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1352: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1353: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1354: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1355: ilink = ilink->next;
1356: }
1357: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1358: } else {
1359: PetscCall(VecSet(y, 0.0));
1360: while (ilink) {
1361: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1362: ilink = ilink->next;
1363: }
1364: }
1365: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1366: PetscCall(VecSet(y, 0.0));
1367: /* solve on first block for first block variables */
1368: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1369: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1370: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1371: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1372: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1373: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1374: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1375: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1377: /* compute the residual only onto second block variables using first block variables */
1378: PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1379: ilink = ilink->next;
1380: PetscCall(VecScale(ilink->x, -1.0));
1381: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1382: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1384: /* solve on second block variables */
1385: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1386: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1387: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1388: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1389: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1390: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1391: } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1392: if (!jac->w1) {
1393: PetscCall(VecDuplicate(x, &jac->w1));
1394: PetscCall(VecDuplicate(x, &jac->w2));
1395: }
1396: PetscCall(VecSet(y, 0.0));
1397: PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1398: cnt = 1;
1399: while (ilink->next) {
1400: ilink = ilink->next;
1401: /* compute the residual only over the part of the vector needed */
1402: PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1403: PetscCall(VecScale(ilink->x, -1.0));
1404: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1405: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1406: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1407: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1408: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1409: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1410: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1411: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1412: }
1413: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1414: cnt -= 2;
1415: while (ilink->previous) {
1416: ilink = ilink->previous;
1417: /* compute the residual only over the part of the vector needed */
1418: PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1419: PetscCall(VecScale(ilink->x, -1.0));
1420: PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1421: PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1422: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1423: PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1424: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1425: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1426: PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1427: PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1428: }
1429: }
1430: } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1431: PetscFunctionReturn(PETSC_SUCCESS);
1432: }
1434: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1435: {
1436: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1437: PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1438: KSP ksp = ilinkA->ksp;
1439: Vec u, v, Hu, d, work1, work2;
1440: PetscScalar alpha, z, nrmz2, *vecz;
1441: PetscReal lowbnd, nu, beta;
1442: PetscInt j, iterGKB;
1444: PetscFunctionBegin;
1445: PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1446: PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1447: PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1448: PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1450: u = jac->u;
1451: v = jac->v;
1452: Hu = jac->Hu;
1453: d = jac->d;
1454: work1 = jac->w1;
1455: work2 = jac->w2;
1456: vecz = jac->vecz;
1458: /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1459: /* Add q = q + nu*B*b */
1460: if (jac->gkbnu) {
1461: nu = jac->gkbnu;
1462: PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1463: PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1464: } else {
1465: /* Situation when no augmented Lagrangian is used. Then we set inner */
1466: /* matrix N = I in [Ar13], and thus nu = 1. */
1467: nu = 1;
1468: }
1470: /* Transform rhs from [q,tilde{b}] to [0,b] */
1471: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1472: PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1473: PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1474: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1475: PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1476: PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x */
1478: /* First step of algorithm */
1479: PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1480: KSPCheckDot(ksp, beta);
1481: beta = PetscSqrtReal(nu) * beta;
1482: PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c */
1483: PetscCall(MatMult(jac->B, v, work2)); /* u = H^{-1}*B*v */
1484: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1485: PetscCall(KSPSolve(ksp, work2, u));
1486: PetscCall(KSPCheckSolve(ksp, pc, u));
1487: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1488: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1489: PetscCall(VecDot(Hu, u, &alpha));
1490: KSPCheckDot(ksp, alpha);
1491: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1492: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1493: PetscCall(VecScale(u, 1.0 / alpha));
1494: PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c */
1496: z = beta / alpha;
1497: vecz[1] = z;
1499: /* Computation of first iterate x(1) and p(1) */
1500: PetscCall(VecAXPY(ilinkA->y, z, u));
1501: PetscCall(VecCopy(d, ilinkD->y));
1502: PetscCall(VecScale(ilinkD->y, -z));
1504: iterGKB = 1;
1505: lowbnd = 2 * jac->gkbtol;
1506: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1508: while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1509: iterGKB += 1;
1510: PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1511: PetscCall(VecAXPBY(v, nu, -alpha, work1));
1512: PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v */
1513: beta = beta / PetscSqrtReal(nu);
1514: PetscCall(VecScale(v, 1.0 / beta));
1515: PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1516: PetscCall(MatMult(jac->H, u, Hu));
1517: PetscCall(VecAXPY(work2, -beta, Hu));
1518: PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1519: PetscCall(KSPSolve(ksp, work2, u));
1520: PetscCall(KSPCheckSolve(ksp, pc, u));
1521: PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1522: PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */
1523: PetscCall(VecDot(Hu, u, &alpha));
1524: KSPCheckDot(ksp, alpha);
1525: PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1526: alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1527: PetscCall(VecScale(u, 1.0 / alpha));
1529: z = -beta / alpha * z; /* z <- beta/alpha*z */
1530: vecz[0] = z;
1532: /* Computation of new iterate x(i+1) and p(i+1) */
1533: PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1534: PetscCall(VecAXPY(ilinkA->y, z, u)); /* r = r + z*u */
1535: PetscCall(VecAXPY(ilinkD->y, -z, d)); /* p = p - z*d */
1536: PetscCall(MatMult(jac->H, ilinkA->y, Hu)); /* ||u||_H = u'*H*u */
1537: PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));
1539: /* Compute Lower Bound estimate */
1540: if (iterGKB > jac->gkbdelay) {
1541: lowbnd = 0.0;
1542: for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1543: lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1544: }
1546: for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1547: if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1548: }
1550: PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1551: PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1552: PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1553: PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1555: PetscFunctionReturn(PETSC_SUCCESS);
1556: }
1558: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1559: ((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) || \
1560: 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) || \
1561: VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))
1563: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1564: {
1565: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1566: PC_FieldSplitLink ilink = jac->head;
1567: PetscInt bs;
1569: PetscFunctionBegin;
1570: if (jac->type == PC_COMPOSITE_ADDITIVE) {
1571: if (jac->defaultsplit) {
1572: PetscCall(VecGetBlockSize(x, &bs));
1573: 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);
1574: PetscCall(VecGetBlockSize(y, &bs));
1575: 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);
1576: PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1577: while (ilink) {
1578: PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1579: PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1580: PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1581: PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1582: ilink = ilink->next;
1583: }
1584: PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1585: } else {
1586: PetscCall(VecSet(y, 0.0));
1587: while (ilink) {
1588: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1589: ilink = ilink->next;
1590: }
1591: }
1592: } else {
1593: if (!jac->w1) {
1594: PetscCall(VecDuplicate(x, &jac->w1));
1595: PetscCall(VecDuplicate(x, &jac->w2));
1596: }
1597: PetscCall(VecSet(y, 0.0));
1598: if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1599: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1600: while (ilink->next) {
1601: ilink = ilink->next;
1602: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1603: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1604: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1605: }
1606: while (ilink->previous) {
1607: ilink = ilink->previous;
1608: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1609: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1610: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1611: }
1612: } else {
1613: while (ilink->next) { /* get to last entry in linked list */
1614: ilink = ilink->next;
1615: }
1616: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1617: while (ilink->previous) {
1618: ilink = ilink->previous;
1619: PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1620: PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1621: PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1622: }
1623: }
1624: }
1625: PetscFunctionReturn(PETSC_SUCCESS);
1626: }
1628: static PetscErrorCode PCReset_FieldSplit(PC pc)
1629: {
1630: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1631: PC_FieldSplitLink ilink = jac->head, next;
1633: PetscFunctionBegin;
1634: while (ilink) {
1635: PetscCall(KSPDestroy(&ilink->ksp));
1636: PetscCall(VecDestroy(&ilink->x));
1637: PetscCall(VecDestroy(&ilink->y));
1638: PetscCall(VecDestroy(&ilink->z));
1639: PetscCall(VecScatterDestroy(&ilink->sctx));
1640: PetscCall(ISDestroy(&ilink->is));
1641: PetscCall(ISDestroy(&ilink->is_col));
1642: PetscCall(PetscFree(ilink->splitname));
1643: PetscCall(PetscFree(ilink->fields));
1644: PetscCall(PetscFree(ilink->fields_col));
1645: next = ilink->next;
1646: PetscCall(PetscFree(ilink));
1647: ilink = next;
1648: }
1649: jac->head = NULL;
1650: PetscCall(PetscFree2(jac->x, jac->y));
1651: if (jac->mat && jac->mat != jac->pmat) {
1652: PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1653: } else if (jac->mat) {
1654: jac->mat = NULL;
1655: }
1656: if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1657: if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1658: jac->nsplits = 0;
1659: PetscCall(VecDestroy(&jac->w1));
1660: PetscCall(VecDestroy(&jac->w2));
1661: PetscCall(MatDestroy(&jac->schur));
1662: PetscCall(MatDestroy(&jac->schurp));
1663: PetscCall(MatDestroy(&jac->schur_user));
1664: PetscCall(KSPDestroy(&jac->kspschur));
1665: PetscCall(KSPDestroy(&jac->kspupper));
1666: PetscCall(MatDestroy(&jac->B));
1667: PetscCall(MatDestroy(&jac->C));
1668: PetscCall(MatDestroy(&jac->H));
1669: PetscCall(VecDestroy(&jac->u));
1670: PetscCall(VecDestroy(&jac->v));
1671: PetscCall(VecDestroy(&jac->Hu));
1672: PetscCall(VecDestroy(&jac->d));
1673: PetscCall(PetscFree(jac->vecz));
1674: PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1675: jac->isrestrict = PETSC_FALSE;
1676: PetscFunctionReturn(PETSC_SUCCESS);
1677: }
1679: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1680: {
1681: PetscFunctionBegin;
1682: PetscCall(PCReset_FieldSplit(pc));
1683: PetscCall(PetscFree(pc->data));
1684: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1685: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1686: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1687: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1688: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1689: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1690: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1691: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1693: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1694: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1695: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1696: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1697: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1698: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1699: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1700: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1701: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1702: PetscFunctionReturn(PETSC_SUCCESS);
1703: }
1705: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1706: {
1707: PetscInt bs;
1708: PetscBool flg;
1709: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1710: PCCompositeType ctype;
1712: PetscFunctionBegin;
1713: PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1714: PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1715: PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1716: if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1717: jac->diag_use_amat = pc->useAmat;
1718: 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));
1719: jac->offdiag_use_amat = pc->useAmat;
1720: 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));
1721: PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1722: PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1723: PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1724: if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1725: /* Only setup fields once */
1726: if ((jac->bs > 0) && (jac->nsplits == 0)) {
1727: /* only allow user to set fields from command line if bs is already known.
1728: otherwise user can set them in PCFieldSplitSetDefaults() */
1729: PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1730: if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1731: }
1732: if (jac->type == PC_COMPOSITE_SCHUR) {
1733: PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1734: if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1735: 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));
1736: PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1737: PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1738: } else if (jac->type == PC_COMPOSITE_GKB) {
1739: PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1740: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1741: PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL));
1742: PetscCheck(jac->gkbnu >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nu cannot be less than 0: value %g", (double)jac->gkbnu);
1743: PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1744: PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1745: }
1746: /*
1747: In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1748: 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
1749: is called on the outer solver in case changes were made in the options database
1751: 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()
1752: 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.
1753: Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.
1755: There could be a negative side effect of calling the KSPSetFromOptions() below.
1757: If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1758: */
1759: if (jac->issetup) {
1760: PC_FieldSplitLink ilink = jac->head;
1761: if (jac->type == PC_COMPOSITE_SCHUR) {
1762: if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1763: if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1764: }
1765: while (ilink) {
1766: if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1767: ilink = ilink->next;
1768: }
1769: }
1770: PetscOptionsHeadEnd();
1771: PetscFunctionReturn(PETSC_SUCCESS);
1772: }
1774: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1775: {
1776: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1777: PC_FieldSplitLink ilink, next = jac->head;
1778: char prefix[128];
1779: PetscInt i;
1781: PetscFunctionBegin;
1782: if (jac->splitdefined) {
1783: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1784: PetscFunctionReturn(PETSC_SUCCESS);
1785: }
1786: for (i = 0; i < n; i++) {
1787: 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);
1788: PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1789: }
1790: PetscCall(PetscNew(&ilink));
1791: if (splitname) {
1792: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1793: } else {
1794: PetscCall(PetscMalloc1(3, &ilink->splitname));
1795: PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1796: }
1797: 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 */
1798: PetscCall(PetscMalloc1(n, &ilink->fields));
1799: PetscCall(PetscArraycpy(ilink->fields, fields, n));
1800: PetscCall(PetscMalloc1(n, &ilink->fields_col));
1801: PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));
1803: ilink->nfields = n;
1804: ilink->next = NULL;
1805: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1806: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1807: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1808: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1809: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1811: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1812: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1814: if (!next) {
1815: jac->head = ilink;
1816: ilink->previous = NULL;
1817: } else {
1818: while (next->next) next = next->next;
1819: next->next = ilink;
1820: ilink->previous = next;
1821: }
1822: jac->nsplits++;
1823: PetscFunctionReturn(PETSC_SUCCESS);
1824: }
1826: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1827: {
1828: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1830: PetscFunctionBegin;
1831: *subksp = NULL;
1832: if (n) *n = 0;
1833: if (jac->type == PC_COMPOSITE_SCHUR) {
1834: PetscInt nn;
1836: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1837: PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1838: nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1839: PetscCall(PetscMalloc1(nn, subksp));
1840: (*subksp)[0] = jac->head->ksp;
1841: (*subksp)[1] = jac->kspschur;
1842: if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1843: if (n) *n = nn;
1844: }
1845: PetscFunctionReturn(PETSC_SUCCESS);
1846: }
1848: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1849: {
1850: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1852: PetscFunctionBegin;
1853: PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1854: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1855: PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));
1857: (*subksp)[1] = jac->kspschur;
1858: if (n) *n = jac->nsplits;
1859: PetscFunctionReturn(PETSC_SUCCESS);
1860: }
1862: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1863: {
1864: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1865: PetscInt cnt = 0;
1866: PC_FieldSplitLink ilink = jac->head;
1868: PetscFunctionBegin;
1869: PetscCall(PetscMalloc1(jac->nsplits, subksp));
1870: while (ilink) {
1871: (*subksp)[cnt++] = ilink->ksp;
1872: ilink = ilink->next;
1873: }
1874: 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);
1875: if (n) *n = jac->nsplits;
1876: PetscFunctionReturn(PETSC_SUCCESS);
1877: }
1879: /*@C
1880: PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.
1882: Input Parameters:
1883: + pc - the preconditioner context
1884: - isy - the index set that defines the indices to which the fieldsplit is to be restricted
1886: Level: advanced
1888: Developer Notes:
1889: It seems the resulting `IS`s will not cover the entire space, so
1890: how can they define a convergent preconditioner? Needs explaining.
1892: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1893: @*/
1894: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1895: {
1896: PetscFunctionBegin;
1899: PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1900: PetscFunctionReturn(PETSC_SUCCESS);
1901: }
1903: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1904: {
1905: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1906: PC_FieldSplitLink ilink = jac->head, next;
1907: PetscInt localsize, size, sizez, i;
1908: const PetscInt *ind, *indz;
1909: PetscInt *indc, *indcz;
1910: PetscBool flg;
1912: PetscFunctionBegin;
1913: PetscCall(ISGetLocalSize(isy, &localsize));
1914: PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1915: size -= localsize;
1916: while (ilink) {
1917: IS isrl, isr;
1918: PC subpc;
1919: PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1920: PetscCall(ISGetLocalSize(isrl, &localsize));
1921: PetscCall(PetscMalloc1(localsize, &indc));
1922: PetscCall(ISGetIndices(isrl, &ind));
1923: PetscCall(PetscArraycpy(indc, ind, localsize));
1924: PetscCall(ISRestoreIndices(isrl, &ind));
1925: PetscCall(ISDestroy(&isrl));
1926: for (i = 0; i < localsize; i++) *(indc + i) += size;
1927: PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1928: PetscCall(PetscObjectReference((PetscObject)isr));
1929: PetscCall(ISDestroy(&ilink->is));
1930: ilink->is = isr;
1931: PetscCall(PetscObjectReference((PetscObject)isr));
1932: PetscCall(ISDestroy(&ilink->is_col));
1933: ilink->is_col = isr;
1934: PetscCall(ISDestroy(&isr));
1935: PetscCall(KSPGetPC(ilink->ksp, &subpc));
1936: PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1937: if (flg) {
1938: IS iszl, isz;
1939: MPI_Comm comm;
1940: PetscCall(ISGetLocalSize(ilink->is, &localsize));
1941: comm = PetscObjectComm((PetscObject)ilink->is);
1942: PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1943: PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1944: sizez -= localsize;
1945: PetscCall(ISGetLocalSize(iszl, &localsize));
1946: PetscCall(PetscMalloc1(localsize, &indcz));
1947: PetscCall(ISGetIndices(iszl, &indz));
1948: PetscCall(PetscArraycpy(indcz, indz, localsize));
1949: PetscCall(ISRestoreIndices(iszl, &indz));
1950: PetscCall(ISDestroy(&iszl));
1951: for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1952: PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1953: PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1954: PetscCall(ISDestroy(&isz));
1955: }
1956: next = ilink->next;
1957: ilink = next;
1958: }
1959: jac->isrestrict = PETSC_TRUE;
1960: PetscFunctionReturn(PETSC_SUCCESS);
1961: }
1963: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1964: {
1965: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1966: PC_FieldSplitLink ilink, next = jac->head;
1967: char prefix[128];
1969: PetscFunctionBegin;
1970: if (jac->splitdefined) {
1971: PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1972: PetscFunctionReturn(PETSC_SUCCESS);
1973: }
1974: PetscCall(PetscNew(&ilink));
1975: if (splitname) {
1976: PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1977: } else {
1978: PetscCall(PetscMalloc1(8, &ilink->splitname));
1979: PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1980: }
1981: 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 */
1982: PetscCall(PetscObjectReference((PetscObject)is));
1983: PetscCall(ISDestroy(&ilink->is));
1984: ilink->is = is;
1985: PetscCall(PetscObjectReference((PetscObject)is));
1986: PetscCall(ISDestroy(&ilink->is_col));
1987: ilink->is_col = is;
1988: ilink->next = NULL;
1989: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1990: PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1991: PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1992: PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1993: PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1995: PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1996: PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1998: if (!next) {
1999: jac->head = ilink;
2000: ilink->previous = NULL;
2001: } else {
2002: while (next->next) next = next->next;
2003: next->next = ilink;
2004: ilink->previous = next;
2005: }
2006: jac->nsplits++;
2007: PetscFunctionReturn(PETSC_SUCCESS);
2008: }
2010: /*@C
2011: PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`
2013: Logically Collective
2015: Input Parameters:
2016: + pc - the preconditioner context
2017: . splitname - name of this split, if `NULL` the number of the split is used
2018: . n - the number of fields in this split
2019: . fields - the fields in this split
2020: - 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
2021: of the matrix and fields_col provides the column indices for that block
2023: Level: intermediate
2025: Notes:
2026: Use `PCFieldSplitSetIS()` to set a general set of indices as a split.
2028: `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2029: 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
2030: 0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2031: where the numbered entries indicate what is in the split.
2033: This function is called once per split (it creates a new split each time). Solve options
2034: for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.
2036: `PCFieldSplitSetIS()` does not support having a fields_col different from fields
2038: Developer Notes:
2039: This routine does not actually create the `IS` representing the split, that is delayed
2040: until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2041: available when this routine is called.
2043: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2044: @*/
2045: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2046: {
2047: PetscFunctionBegin;
2049: PetscAssertPointer(splitname, 2);
2050: PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2051: PetscAssertPointer(fields, 4);
2052: PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2053: PetscFunctionReturn(PETSC_SUCCESS);
2054: }
2056: /*@
2057: PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2058: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2060: Logically Collective
2062: Input Parameters:
2063: + pc - the preconditioner object
2064: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2066: Options Database Key:
2067: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks
2069: Level: intermediate
2071: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2072: @*/
2073: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2074: {
2075: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2076: PetscBool isfs;
2078: PetscFunctionBegin;
2080: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2081: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2082: jac->diag_use_amat = flg;
2083: PetscFunctionReturn(PETSC_SUCCESS);
2084: }
2086: /*@
2087: PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2088: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2090: Logically Collective
2092: Input Parameter:
2093: . pc - the preconditioner object
2095: Output Parameter:
2096: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2098: Level: intermediate
2100: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2101: @*/
2102: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2103: {
2104: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2105: PetscBool isfs;
2107: PetscFunctionBegin;
2109: PetscAssertPointer(flg, 2);
2110: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2111: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2112: *flg = jac->diag_use_amat;
2113: PetscFunctionReturn(PETSC_SUCCESS);
2114: }
2116: /*@
2117: PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2118: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2120: Logically Collective
2122: Input Parameters:
2123: + pc - the preconditioner object
2124: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2126: Options Database Key:
2127: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks
2129: Level: intermediate
2131: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2132: @*/
2133: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2134: {
2135: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2136: PetscBool isfs;
2138: PetscFunctionBegin;
2140: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2141: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2142: jac->offdiag_use_amat = flg;
2143: PetscFunctionReturn(PETSC_SUCCESS);
2144: }
2146: /*@
2147: PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2148: the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2150: Logically Collective
2152: Input Parameter:
2153: . pc - the preconditioner object
2155: Output Parameter:
2156: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2158: Level: intermediate
2160: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2161: @*/
2162: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2163: {
2164: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2165: PetscBool isfs;
2167: PetscFunctionBegin;
2169: PetscAssertPointer(flg, 2);
2170: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2171: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2172: *flg = jac->offdiag_use_amat;
2173: PetscFunctionReturn(PETSC_SUCCESS);
2174: }
2176: /*@C
2177: PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`
2179: Logically Collective
2181: Input Parameters:
2182: + pc - the preconditioner context
2183: . splitname - name of this split, if `NULL` the number of the split is used
2184: - is - the index set that defines the elements in this split
2186: Level: intermediate
2188: Notes:
2189: Use `PCFieldSplitSetFields()`, for splits defined by strided types.
2191: This function is called once per split (it creates a new split each time). Solve options
2192: for this split will be available under the prefix -fieldsplit_SPLITNAME_.
2194: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2195: @*/
2196: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2197: {
2198: PetscFunctionBegin;
2200: if (splitname) PetscAssertPointer(splitname, 2);
2202: PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2203: PetscFunctionReturn(PETSC_SUCCESS);
2204: }
2206: /*@C
2207: PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`
2209: Logically Collective
2211: Input Parameters:
2212: + pc - the preconditioner context
2213: - splitname - name of this split
2215: Output Parameter:
2216: . is - the index set that defines the elements in this split, or `NULL` if the split is not found
2218: Level: intermediate
2220: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2221: @*/
2222: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2223: {
2224: PetscFunctionBegin;
2226: PetscAssertPointer(splitname, 2);
2227: PetscAssertPointer(is, 3);
2228: {
2229: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2230: PC_FieldSplitLink ilink = jac->head;
2231: PetscBool found;
2233: *is = NULL;
2234: while (ilink) {
2235: PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2236: if (found) {
2237: *is = ilink->is;
2238: break;
2239: }
2240: ilink = ilink->next;
2241: }
2242: }
2243: PetscFunctionReturn(PETSC_SUCCESS);
2244: }
2246: /*@C
2247: PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`
2249: Logically Collective
2251: Input Parameters:
2252: + pc - the preconditioner context
2253: - index - index of this split
2255: Output Parameter:
2256: . is - the index set that defines the elements in this split
2258: Level: intermediate
2260: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2261: @*/
2262: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2263: {
2264: PetscFunctionBegin;
2265: PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2267: PetscAssertPointer(is, 3);
2268: {
2269: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2270: PC_FieldSplitLink ilink = jac->head;
2271: PetscInt i = 0;
2272: PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);
2274: while (i < index) {
2275: ilink = ilink->next;
2276: ++i;
2277: }
2278: PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2279: }
2280: PetscFunctionReturn(PETSC_SUCCESS);
2281: }
2283: /*@
2284: PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2285: fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.
2287: Logically Collective
2289: Input Parameters:
2290: + pc - the preconditioner context
2291: - bs - the block size
2293: Level: intermediate
2295: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2296: @*/
2297: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2298: {
2299: PetscFunctionBegin;
2302: PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2303: PetscFunctionReturn(PETSC_SUCCESS);
2304: }
2306: /*@C
2307: PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits
2309: Collective
2311: Input Parameter:
2312: . pc - the preconditioner context
2314: Output Parameters:
2315: + n - the number of splits
2316: - subksp - the array of `KSP` contexts
2318: Level: advanced
2320: Notes:
2321: After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2322: (not the `KSP`, just the array that contains them).
2324: You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.
2326: If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2327: Schur complement and the `KSP` object used to iterate over the Schur complement.
2328: To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.
2330: If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2331: inner linear system defined by the matrix H in each loop.
2333: Fortran Notes:
2334: You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2335: You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2336: `KSP` array must be.
2338: Developer Notes:
2339: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2341: The Fortran interface should be modernized to return directly the array of values.
2343: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2344: @*/
2345: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2346: {
2347: PetscFunctionBegin;
2349: if (n) PetscAssertPointer(n, 2);
2350: PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2351: PetscFunctionReturn(PETSC_SUCCESS);
2352: }
2354: /*@C
2355: PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`
2357: Collective
2359: Input Parameter:
2360: . pc - the preconditioner context
2362: Output Parameters:
2363: + n - the number of splits
2364: - subksp - the array of `KSP` contexts
2366: Level: advanced
2368: Notes:
2369: After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2370: (not the `KSP` just the array that contains them).
2372: You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.
2374: If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2375: + 1 - the `KSP` used for the (1,1) block
2376: . 2 - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2377: - 3 - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).
2379: It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.
2381: Fortran Notes:
2382: You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2383: You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2384: `KSP` array must be.
2386: Developer Notes:
2387: There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2389: Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?
2391: The Fortran interface should be modernized to return directly the array of values.
2393: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2394: @*/
2395: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2396: {
2397: PetscFunctionBegin;
2399: if (n) PetscAssertPointer(n, 2);
2400: PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2401: PetscFunctionReturn(PETSC_SUCCESS);
2402: }
2404: /*@
2405: PCFieldSplitSetSchurPre - Indicates from what operator the preconditioner is constructed for the Schur complement.
2406: The default is the A11 matrix.
2408: Collective
2410: Input Parameters:
2411: + pc - the preconditioner context
2412: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2413: `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2414: `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2415: - pre - matrix to use for preconditioning, or `NULL`
2417: Options Database Keys:
2418: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2419: - -fieldsplit_1_pc_type <pctype> - the preconditioner algorithm that is used to construct the preconditioner from the operator
2421: Level: intermediate
2423: Notes:
2424: If ptype is
2425: + a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2426: matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2427: . self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2428: The only preconditioner that currently works with this symbolic representation matrix object is the `PCLSC`
2429: preconditioner
2430: . user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2431: to this function).
2432: . selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2433: This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2434: lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2435: - full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2436: computed internally by `PCFIELDSPLIT` (this is expensive)
2437: useful mostly as a test that the Schur complement approach can work for your problem
2439: When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2440: with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2441: `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.
2443: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2444: `MatSchurComplementSetAinvType()`, `PCLSC`,
2446: @*/
2447: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2448: {
2449: PetscFunctionBegin;
2451: PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2452: PetscFunctionReturn(PETSC_SUCCESS);
2453: }
2455: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2456: {
2457: return PCFieldSplitSetSchurPre(pc, ptype, pre);
2458: } /* Deprecated name */
2460: /*@
2461: PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2462: preconditioned. See `PCFieldSplitSetSchurPre()` for details.
2464: Logically Collective
2466: Input Parameter:
2467: . pc - the preconditioner context
2469: Output Parameters:
2470: + 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`
2471: - pre - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`
2473: Level: intermediate
2475: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2477: @*/
2478: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2479: {
2480: PetscFunctionBegin;
2482: PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2483: PetscFunctionReturn(PETSC_SUCCESS);
2484: }
2486: /*@
2487: PCFieldSplitSchurGetS - extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately
2489: Not Collective
2491: Input Parameter:
2492: . pc - the preconditioner context
2494: Output Parameter:
2495: . S - the Schur complement matrix
2497: Level: advanced
2499: Note:
2500: This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.
2502: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2503: `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2504: @*/
2505: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2506: {
2507: const char *t;
2508: PetscBool isfs;
2509: PC_FieldSplit *jac;
2511: PetscFunctionBegin;
2513: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2514: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2515: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2516: jac = (PC_FieldSplit *)pc->data;
2517: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2518: if (S) *S = jac->schur;
2519: PetscFunctionReturn(PETSC_SUCCESS);
2520: }
2522: /*@
2523: PCFieldSplitSchurRestoreS - returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`
2525: Not Collective
2527: Input Parameters:
2528: + pc - the preconditioner context
2529: - S - the Schur complement matrix
2531: Level: advanced
2533: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2534: @*/
2535: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2536: {
2537: const char *t;
2538: PetscBool isfs;
2539: PC_FieldSplit *jac;
2541: PetscFunctionBegin;
2543: PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2544: PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2545: PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2546: jac = (PC_FieldSplit *)pc->data;
2547: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2548: PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2549: PetscFunctionReturn(PETSC_SUCCESS);
2550: }
2552: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2553: {
2554: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2556: PetscFunctionBegin;
2557: jac->schurpre = ptype;
2558: if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2559: PetscCall(MatDestroy(&jac->schur_user));
2560: jac->schur_user = pre;
2561: PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2562: }
2563: PetscFunctionReturn(PETSC_SUCCESS);
2564: }
2566: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2567: {
2568: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2570: PetscFunctionBegin;
2571: if (ptype) *ptype = jac->schurpre;
2572: if (pre) *pre = jac->schur_user;
2573: PetscFunctionReturn(PETSC_SUCCESS);
2574: }
2576: /*@
2577: PCFieldSplitSetSchurFactType - sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`
2579: Collective
2581: Input Parameters:
2582: + pc - the preconditioner context
2583: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default
2585: Options Database Key:
2586: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`
2588: Level: intermediate
2590: Notes:
2591: The FULL factorization is
2592: .vb
2593: (A B) = (1 0) (A 0) (1 Ainv*B) = L D U
2594: (C E) (C*Ainv 1) (0 S) (0 1)
2595: .vb
2596: 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 $L*D$,
2597: and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations,
2598: thus allowing the use of `KSPMINRES)`. Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.
2600: If A and S are solved exactly
2601: .vb
2602: *) FULL factorization is a direct solver.
2603: *) 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.
2604: *) 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.
2605: .ve
2607: If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2608: application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.
2610: For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.
2612: A flexible method like `KSPFGMRES` or `KSPGCR`, [](sec_flexibleksp), must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used to solve with A or S).
2614: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2615: [](sec_flexibleksp)
2616: @*/
2617: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2618: {
2619: PetscFunctionBegin;
2621: PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2622: PetscFunctionReturn(PETSC_SUCCESS);
2623: }
2625: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2626: {
2627: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2629: PetscFunctionBegin;
2630: jac->schurfactorization = ftype;
2631: PetscFunctionReturn(PETSC_SUCCESS);
2632: }
2634: /*@
2635: PCFieldSplitSetSchurScale - Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.
2637: Collective
2639: Input Parameters:
2640: + pc - the preconditioner context
2641: - scale - scaling factor for the Schur complement
2643: Options Database Key:
2644: . -pc_fieldsplit_schur_scale <scale> - default is -1.0
2646: Level: intermediate
2648: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2649: @*/
2650: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2651: {
2652: PetscFunctionBegin;
2655: PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2656: PetscFunctionReturn(PETSC_SUCCESS);
2657: }
2659: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2660: {
2661: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2663: PetscFunctionBegin;
2664: jac->schurscale = scale;
2665: PetscFunctionReturn(PETSC_SUCCESS);
2666: }
2668: /*@C
2669: PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
2671: Collective
2673: Input Parameter:
2674: . pc - the preconditioner context
2676: Output Parameters:
2677: + A00 - the (0,0) block
2678: . A01 - the (0,1) block
2679: . A10 - the (1,0) block
2680: - A11 - the (1,1) block
2682: Level: advanced
2684: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2685: @*/
2686: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2687: {
2688: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2690: PetscFunctionBegin;
2692: PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2693: if (A00) *A00 = jac->pmat[0];
2694: if (A01) *A01 = jac->B;
2695: if (A10) *A10 = jac->C;
2696: if (A11) *A11 = jac->pmat[1];
2697: PetscFunctionReturn(PETSC_SUCCESS);
2698: }
2700: /*@
2701: PCFieldSplitSetGKBTol - Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2703: Collective
2705: Input Parameters:
2706: + pc - the preconditioner context
2707: - tolerance - the solver tolerance
2709: Options Database Key:
2710: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5
2712: Level: intermediate
2714: Note:
2715: The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2716: It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2717: this estimate, the stopping criterion is satisfactory in practical cases.
2719: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2720: @*/
2721: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2722: {
2723: PetscFunctionBegin;
2726: PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2727: PetscFunctionReturn(PETSC_SUCCESS);
2728: }
2730: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2731: {
2732: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2734: PetscFunctionBegin;
2735: jac->gkbtol = tolerance;
2736: PetscFunctionReturn(PETSC_SUCCESS);
2737: }
2739: /*@
2740: PCFieldSplitSetGKBMaxit - Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`
2742: Collective
2744: Input Parameters:
2745: + pc - the preconditioner context
2746: - maxit - the maximum number of iterations
2748: Options Database Key:
2749: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100
2751: Level: intermediate
2753: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2754: @*/
2755: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2756: {
2757: PetscFunctionBegin;
2760: PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2761: PetscFunctionReturn(PETSC_SUCCESS);
2762: }
2764: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2765: {
2766: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2768: PetscFunctionBegin;
2769: jac->gkbmaxit = maxit;
2770: PetscFunctionReturn(PETSC_SUCCESS);
2771: }
2773: /*@
2774: PCFieldSplitSetGKBDelay - Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2775: preconditioner.
2777: Collective
2779: Input Parameters:
2780: + pc - the preconditioner context
2781: - delay - the delay window in the lower bound estimate
2783: Options Database Key:
2784: . -pc_fieldsplit_gkb_delay <delay> - default is 5
2786: Level: intermediate
2788: Notes:
2789: 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 $
2790: is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2791: at least (`delay` + 1) iterations to stop.
2793: For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`
2795: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2796: @*/
2797: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2798: {
2799: PetscFunctionBegin;
2802: PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2803: PetscFunctionReturn(PETSC_SUCCESS);
2804: }
2806: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2807: {
2808: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2810: PetscFunctionBegin;
2811: jac->gkbdelay = delay;
2812: PetscFunctionReturn(PETSC_SUCCESS);
2813: }
2815: /*@
2816: PCFieldSplitSetGKBNu - Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2817: Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2819: Collective
2821: Input Parameters:
2822: + pc - the preconditioner context
2823: - nu - the shift parameter
2825: Options Database Key:
2826: . -pc_fieldsplit_gkb_nu <nu> - default is 1
2828: Level: intermediate
2830: Notes:
2831: This shift is in general done to obtain better convergence properties for the outer loop of the algorithm. This is often achieved by choosing `nu` sufficiently large. However,
2832: if `nu` is chosen too large, the matrix H might be badly conditioned and the solution of the linear system $Hx = b$ in the inner loop becomes difficult. It is therefore
2833: necessary to find a good balance in between the convergence of the inner and outer loop.
2835: For `nu` = 0, no shift is done. In this case A00 has to be positive definite. The matrix N in {cite}`arioli2013` is then chosen as identity.
2837: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2838: @*/
2839: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2840: {
2841: PetscFunctionBegin;
2844: PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2845: PetscFunctionReturn(PETSC_SUCCESS);
2846: }
2848: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2849: {
2850: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2852: PetscFunctionBegin;
2853: jac->gkbnu = nu;
2854: PetscFunctionReturn(PETSC_SUCCESS);
2855: }
2857: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2858: {
2859: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2861: PetscFunctionBegin;
2862: jac->type = type;
2863: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2864: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2865: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2866: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2867: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2868: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2869: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2870: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2871: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2873: if (type == PC_COMPOSITE_SCHUR) {
2874: pc->ops->apply = PCApply_FieldSplit_Schur;
2875: pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2876: pc->ops->view = PCView_FieldSplit_Schur;
2878: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2879: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2880: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2881: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2882: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2883: } else if (type == PC_COMPOSITE_GKB) {
2884: pc->ops->apply = PCApply_FieldSplit_GKB;
2885: pc->ops->view = PCView_FieldSplit_GKB;
2887: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2888: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2889: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2890: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2891: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2892: } else {
2893: pc->ops->apply = PCApply_FieldSplit;
2894: pc->ops->view = PCView_FieldSplit;
2896: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2897: }
2898: PetscFunctionReturn(PETSC_SUCCESS);
2899: }
2901: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2902: {
2903: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2905: PetscFunctionBegin;
2906: PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2907: 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);
2908: jac->bs = bs;
2909: PetscFunctionReturn(PETSC_SUCCESS);
2910: }
2912: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2913: {
2914: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2915: PC_FieldSplitLink ilink_current = jac->head;
2916: IS is_owned;
2918: PetscFunctionBegin;
2919: jac->coordinates_set = PETSC_TRUE; // Internal flag
2920: PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));
2922: while (ilink_current) {
2923: // For each IS, embed it to get local coords indces
2924: IS is_coords;
2925: PetscInt ndofs_block;
2926: const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block
2928: // Setting drop to true for safety. It should make no difference.
2929: PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2930: PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2931: PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));
2933: // Allocate coordinates vector and set it directly
2934: PetscCall(PetscMalloc1(ndofs_block * dim, &(ilink_current->coords)));
2935: for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2936: for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2937: }
2938: ilink_current->dim = dim;
2939: ilink_current->ndofs = ndofs_block;
2940: PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2941: PetscCall(ISDestroy(&is_coords));
2942: ilink_current = ilink_current->next;
2943: }
2944: PetscCall(ISDestroy(&is_owned));
2945: PetscFunctionReturn(PETSC_SUCCESS);
2946: }
2948: /*@
2949: PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2951: Collective
2953: Input Parameters:
2954: + pc - the preconditioner context
2955: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2957: Options Database Key:
2958: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
2960: Level: intermediate
2962: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2963: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2964: @*/
2965: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2966: {
2967: PetscFunctionBegin;
2969: PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2970: PetscFunctionReturn(PETSC_SUCCESS);
2971: }
2973: /*@
2974: PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2976: Not collective
2978: Input Parameter:
2979: . pc - the preconditioner context
2981: Output Parameter:
2982: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2984: Level: intermediate
2986: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2987: `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2988: @*/
2989: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2990: {
2991: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2993: PetscFunctionBegin;
2995: PetscAssertPointer(type, 2);
2996: *type = jac->type;
2997: PetscFunctionReturn(PETSC_SUCCESS);
2998: }
3000: /*@
3001: PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3003: Logically Collective
3005: Input Parameters:
3006: + pc - the preconditioner context
3007: - flg - boolean indicating whether to use field splits defined by the `DM`
3009: Options Database Key:
3010: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`
3012: Level: intermediate
3014: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3015: @*/
3016: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3017: {
3018: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3019: PetscBool isfs;
3021: PetscFunctionBegin;
3024: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3025: if (isfs) jac->dm_splits = flg;
3026: PetscFunctionReturn(PETSC_SUCCESS);
3027: }
3029: /*@
3030: PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3032: Logically Collective
3034: Input Parameter:
3035: . pc - the preconditioner context
3037: Output Parameter:
3038: . flg - boolean indicating whether to use field splits defined by the `DM`
3040: Level: intermediate
3042: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3043: @*/
3044: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3045: {
3046: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3047: PetscBool isfs;
3049: PetscFunctionBegin;
3051: PetscAssertPointer(flg, 2);
3052: PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3053: if (isfs) {
3054: if (flg) *flg = jac->dm_splits;
3055: }
3056: PetscFunctionReturn(PETSC_SUCCESS);
3057: }
3059: /*@
3060: PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3062: Logically Collective
3064: Input Parameter:
3065: . pc - the preconditioner context
3067: Output Parameter:
3068: . flg - boolean indicating whether to detect fields or not
3070: Level: intermediate
3072: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3073: @*/
3074: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3075: {
3076: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3078: PetscFunctionBegin;
3079: *flg = jac->detect;
3080: PetscFunctionReturn(PETSC_SUCCESS);
3081: }
3083: /*@
3084: PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3086: Logically Collective
3088: Input Parameter:
3089: . pc - the preconditioner context
3091: Output Parameter:
3092: . flg - boolean indicating whether to detect fields or not
3094: Options Database Key:
3095: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point
3097: Level: intermediate
3099: Note:
3100: Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).
3102: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3103: @*/
3104: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3105: {
3106: PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3108: PetscFunctionBegin;
3109: jac->detect = flg;
3110: if (jac->detect) {
3111: PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3112: PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3113: }
3114: PetscFunctionReturn(PETSC_SUCCESS);
3115: }
3117: /*MC
3118: PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3119: collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.
3121: Options Database Keys:
3122: + -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split
3123: . -pc_fieldsplit_default - automatically add any fields to additional splits that have not
3124: been supplied explicitly by `-pc_fieldsplit_%d_fields`
3125: . -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
3126: . -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3127: . -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()`
3128: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`;
3129: see `PCFieldSplitSetSchurFactType()`
3130: - -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver
3132: Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3133: The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3134: For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.
3136: To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3137: options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`
3139: To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3140: and set the options directly on the resulting `KSP` object
3142: Level: intermediate
3144: Notes:
3145: Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3146: to define a split by an arbitrary collection of entries.
3148: If no splits are set the default is used. The splits are defined by entries strided by bs,
3149: beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3150: if this is not called the block size defaults to the blocksize of the second matrix passed
3151: to `KSPSetOperators()`/`PCSetOperators()`.
3153: For the Schur complement preconditioner if
3155: ```{math}
3156: J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3157: ```
3159: the preconditioner using `full` factorization is logically
3160: ```{math}
3161: \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
3162: ```
3163: where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`. $S$ is the Schur complement
3164: ```{math}
3165: S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3166: ```
3167: 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
3168: in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3169: it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3170: $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.
3172: The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3173: `diag` gives
3174: ```{math}
3175: \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & -\text{ksp}(S) \end{array}\right]
3176: ```
3177: 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
3178: can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3179: ```{math}
3180: \left[\begin{array}{cc} A_{00} & 0 \\ A_{10} & S \end{array}\right]
3181: ```
3182: where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3183: ```{math}
3184: \left[\begin{array}{cc} A_{00} & A_{01} \\ 0 & S \end{array}\right]
3185: ```
3186: where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.
3188: If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3189: is used automatically for a second block.
3191: The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3192: Generally it should be used with the `MATAIJ` format.
3194: The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3195: for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3196: One can also use `PCFIELDSPLIT`
3197: inside a smoother resulting in "Distributive Smoothers".
3199: See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.
3201: The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3202: residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.
3204: The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3205: ```{math}
3206: \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3207: ```
3208: 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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3209: 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_`.
3211: Developer Note:
3212: The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3213: user API.
3215: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3216: `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3217: `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3218: `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3219: M*/
3221: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3222: {
3223: PC_FieldSplit *jac;
3225: PetscFunctionBegin;
3226: PetscCall(PetscNew(&jac));
3228: jac->bs = -1;
3229: jac->nsplits = 0;
3230: jac->type = PC_COMPOSITE_MULTIPLICATIVE;
3231: jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3232: jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3233: jac->schurscale = -1.0;
3234: jac->dm_splits = PETSC_TRUE;
3235: jac->detect = PETSC_FALSE;
3236: jac->gkbtol = 1e-5;
3237: jac->gkbdelay = 5;
3238: jac->gkbnu = 1;
3239: jac->gkbmaxit = 100;
3240: jac->gkbmonitor = PETSC_FALSE;
3241: jac->coordinates_set = PETSC_FALSE;
3243: pc->data = (void *)jac;
3245: pc->ops->apply = PCApply_FieldSplit;
3246: pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3247: pc->ops->setup = PCSetUp_FieldSplit;
3248: pc->ops->reset = PCReset_FieldSplit;
3249: pc->ops->destroy = PCDestroy_FieldSplit;
3250: pc->ops->setfromoptions = PCSetFromOptions_FieldSplit;
3251: pc->ops->view = PCView_FieldSplit;
3252: pc->ops->applyrichardson = NULL;
3254: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3255: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3256: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3257: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3258: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3259: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3260: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3261: PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3262: PetscFunctionReturn(PETSC_SUCCESS);
3263: }