1 #include <petsc/private/pcimpl.h> /*I "petscpc.h" I*/ 2 #include <petsc/private/kspimpl.h> /* This is needed to provide the appropriate PETSC_EXTERN for KSP_Solve_FS ....*/ 3 #include <petscdm.h> 4 #include <petscdevice.h> 5 #if PetscDefined(HAVE_CUDA) 6 #include <petscdevice_cuda.h> 7 #endif 8 #if PetscDefined(HAVE_HIP) 9 #include <petscdevice_hip.h> 10 #endif 11 12 const char *const PCFieldSplitSchurPreTypes[] = {"SELF", "SELFP", "A11", "USER", "FULL", "PCFieldSplitSchurPreType", "PC_FIELDSPLIT_SCHUR_PRE_", NULL}; 13 const char *const PCFieldSplitSchurFactTypes[] = {"DIAG", "LOWER", "UPPER", "FULL", "PCFieldSplitSchurFactType", "PC_FIELDSPLIT_SCHUR_FACT_", NULL}; 14 15 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; 16 17 typedef struct _PC_FieldSplitLink *PC_FieldSplitLink; 18 struct _PC_FieldSplitLink { 19 KSP ksp; 20 Vec x, y, z; 21 char *splitname; 22 PetscInt nfields; 23 PetscInt *fields, *fields_col; 24 VecScatter sctx; 25 IS is, is_col; 26 PC_FieldSplitLink next, previous; 27 PetscLogEvent event; 28 29 /* Used only when setting coordinates with PCSetCoordinates */ 30 PetscInt dim; 31 PetscInt ndofs; 32 PetscReal *coords; 33 }; 34 35 typedef struct { 36 PCCompositeType type; 37 PetscBool defaultsplit; /* Flag for a system with a set of 'k' scalar fields with the same layout (and bs = k) */ 38 PetscBool splitdefined; /* Flag is set after the splits have been defined, to prevent more splits from being added */ 39 PetscInt bs; /* Block size for IS and Mat structures */ 40 PetscInt nsplits; /* Number of field divisions defined */ 41 Vec *x, *y, w1, w2; 42 Mat *mat; /* The diagonal block for each split */ 43 Mat *pmat; /* The preconditioning diagonal block for each split */ 44 Mat *Afield; /* The rows of the matrix associated with each split */ 45 PetscBool issetup; 46 47 /* Only used when Schur complement preconditioning is used */ 48 Mat B; /* The (0,1) block */ 49 Mat C; /* The (1,0) block */ 50 Mat schur; /* The Schur complement S = A11 - A10 A00^{-1} A01, the KSP here, kspinner, is H_1 in [El08] */ 51 Mat schurp; /* Assembled approximation to S built by MatSchurComplement to be used as a preconditioning matrix when solving with S */ 52 Mat schur_user; /* User-provided preconditioning matrix for the Schur complement */ 53 PCFieldSplitSchurPreType schurpre; /* Determines which preconditioning matrix is used for the Schur complement */ 54 PCFieldSplitSchurFactType schurfactorization; 55 KSP kspschur; /* The solver for S */ 56 KSP kspupper; /* The solver for A in the upper diagonal part of the factorization (H_2 in [El08]) */ 57 PetscScalar schurscale; /* Scaling factor for the Schur complement solution with DIAG factorization */ 58 59 /* Only used when Golub-Kahan bidiagonalization preconditioning is used */ 60 Mat H; /* The modified matrix H = A00 + nu*A01*A01' */ 61 PetscReal gkbtol; /* Stopping tolerance for lower bound estimate */ 62 PetscInt gkbdelay; /* The delay window for the stopping criterion */ 63 PetscReal gkbnu; /* Parameter for augmented Lagrangian H = A + nu*A01*A01' */ 64 PetscInt gkbmaxit; /* Maximum number of iterations for outer loop */ 65 PetscBool gkbmonitor; /* Monitor for gkb iterations and the lower bound error */ 66 PetscViewer gkbviewer; /* Viewer context for gkbmonitor */ 67 Vec u, v, d, Hu; /* Work vectors for the GKB algorithm */ 68 PetscScalar *vecz; /* Contains intermediate values, eg for lower bound */ 69 70 PC_FieldSplitLink head; 71 PetscBool isrestrict; /* indicates PCFieldSplitRestrictIS() has been last called on this object, hack */ 72 PetscBool suboptionsset; /* Indicates that the KSPSetFromOptions() has been called on the sub-KSPs */ 73 PetscBool dm_splits; /* Whether to use DMCreateFieldDecomposition() whenever possible */ 74 PetscBool diag_use_amat; /* Whether to extract diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */ 75 PetscBool offdiag_use_amat; /* Whether to extract off-diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */ 76 PetscBool detect; /* Whether to form 2-way split by finding zero diagonal entries */ 77 PetscBool coordinates_set; /* Whether PCSetCoordinates has been called */ 78 } PC_FieldSplit; 79 80 /* 81 Note: 82 there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of 83 inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the 84 PC you could change this. 85 */ 86 87 /* This helper is so that setting a user-provided preconditioning matrix is orthogonal to choosing to use it. This way the 88 * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */ 89 static Mat FieldSplitSchurPre(PC_FieldSplit *jac) 90 { 91 switch (jac->schurpre) { 92 case PC_FIELDSPLIT_SCHUR_PRE_SELF: 93 return jac->schur; 94 case PC_FIELDSPLIT_SCHUR_PRE_SELFP: 95 return jac->schurp; 96 case PC_FIELDSPLIT_SCHUR_PRE_A11: 97 return jac->pmat[1]; 98 case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */ 99 case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */ 100 default: 101 return jac->schur_user ? jac->schur_user : jac->pmat[1]; 102 } 103 } 104 105 #include <petscdraw.h> 106 static PetscErrorCode PCView_FieldSplit(PC pc, PetscViewer viewer) 107 { 108 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 109 PetscBool iascii, isdraw; 110 PetscInt i, j; 111 PC_FieldSplitLink ilink = jac->head; 112 113 PetscFunctionBegin; 114 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii)); 115 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw)); 116 if (iascii) { 117 if (jac->bs > 0) { 118 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs)); 119 } else { 120 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits)); 121 } 122 if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n")); 123 if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for diagonal blocks\n")); 124 if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for off-diagonal blocks\n")); 125 PetscCall(PetscViewerASCIIPrintf(viewer, " Solver info for each split is in the following KSP objects:\n")); 126 for (i = 0; i < jac->nsplits; i++) { 127 if (ilink->fields) { 128 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i)); 129 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE)); 130 for (j = 0; j < ilink->nfields; j++) { 131 if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ",")); 132 PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j])); 133 } 134 PetscCall(PetscViewerASCIIPrintf(viewer, "\n")); 135 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE)); 136 } else { 137 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i)); 138 } 139 PetscCall(KSPView(ilink->ksp, viewer)); 140 ilink = ilink->next; 141 } 142 } 143 144 if (isdraw) { 145 PetscDraw draw; 146 PetscReal x, y, w, wd; 147 148 PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw)); 149 PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y)); 150 w = 2 * PetscMin(1.0 - x, x); 151 wd = w / (jac->nsplits + 1); 152 x = x - wd * (jac->nsplits - 1) / 2.0; 153 for (i = 0; i < jac->nsplits; i++) { 154 PetscCall(PetscDrawPushCurrentPoint(draw, x, y)); 155 PetscCall(KSPView(ilink->ksp, viewer)); 156 PetscCall(PetscDrawPopCurrentPoint(draw)); 157 x += wd; 158 ilink = ilink->next; 159 } 160 } 161 PetscFunctionReturn(PETSC_SUCCESS); 162 } 163 164 static PetscErrorCode PCView_FieldSplit_Schur(PC pc, PetscViewer viewer) 165 { 166 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 167 PetscBool iascii, isdraw; 168 PetscInt i, j; 169 PC_FieldSplitLink ilink = jac->head; 170 MatSchurComplementAinvType atype; 171 172 PetscFunctionBegin; 173 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii)); 174 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw)); 175 if (iascii) { 176 if (jac->bs > 0) { 177 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with Schur preconditioner, blocksize = %" PetscInt_FMT ", factorization %s\n", jac->bs, PCFieldSplitSchurFactTypes[jac->schurfactorization])); 178 } else { 179 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with Schur preconditioner, factorization %s\n", PCFieldSplitSchurFactTypes[jac->schurfactorization])); 180 } 181 if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n")); 182 switch (jac->schurpre) { 183 case PC_FIELDSPLIT_SCHUR_PRE_SELF: 184 PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from S itself\n")); 185 break; 186 case PC_FIELDSPLIT_SCHUR_PRE_SELFP: 187 if (jac->schur) { 188 PetscCall(MatSchurComplementGetAinvType(jac->schur, &atype)); 189 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 ")))); 190 } 191 break; 192 case PC_FIELDSPLIT_SCHUR_PRE_A11: 193 PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from A11\n")); 194 break; 195 case PC_FIELDSPLIT_SCHUR_PRE_FULL: 196 PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from the exact Schur complement\n")); 197 break; 198 case PC_FIELDSPLIT_SCHUR_PRE_USER: 199 if (jac->schur_user) { 200 PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from user provided matrix\n")); 201 } else { 202 PetscCall(PetscViewerASCIIPrintf(viewer, " Preconditioner for the Schur complement formed from A11\n")); 203 } 204 break; 205 default: 206 SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Invalid Schur preconditioning type: %d", jac->schurpre); 207 } 208 PetscCall(PetscViewerASCIIPrintf(viewer, " Split info:\n")); 209 PetscCall(PetscViewerASCIIPushTab(viewer)); 210 for (i = 0; i < jac->nsplits; i++) { 211 if (ilink->fields) { 212 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i)); 213 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE)); 214 for (j = 0; j < ilink->nfields; j++) { 215 if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ",")); 216 PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j])); 217 } 218 PetscCall(PetscViewerASCIIPrintf(viewer, "\n")); 219 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE)); 220 } else { 221 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i)); 222 } 223 ilink = ilink->next; 224 } 225 PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for A00 block\n")); 226 PetscCall(PetscViewerASCIIPushTab(viewer)); 227 if (jac->head) { 228 PetscCall(KSPView(jac->head->ksp, viewer)); 229 } else PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n")); 230 PetscCall(PetscViewerASCIIPopTab(viewer)); 231 if (jac->head && jac->kspupper != jac->head->ksp) { 232 PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for upper A00 in upper triangular factor\n")); 233 PetscCall(PetscViewerASCIIPushTab(viewer)); 234 if (jac->kspupper) PetscCall(KSPView(jac->kspupper, viewer)); 235 else PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n")); 236 PetscCall(PetscViewerASCIIPopTab(viewer)); 237 } 238 PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for S = A11 - A10 inv(A00) A01\n")); 239 PetscCall(PetscViewerASCIIPushTab(viewer)); 240 if (jac->kspschur) { 241 PetscCall(KSPView(jac->kspschur, viewer)); 242 } else { 243 PetscCall(PetscViewerASCIIPrintf(viewer, " not yet available\n")); 244 } 245 PetscCall(PetscViewerASCIIPopTab(viewer)); 246 PetscCall(PetscViewerASCIIPopTab(viewer)); 247 } else if (isdraw && jac->head) { 248 PetscDraw draw; 249 PetscReal x, y, w, wd, h; 250 PetscInt cnt = 2; 251 char str[32]; 252 253 PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw)); 254 PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y)); 255 if (jac->kspupper != jac->head->ksp) cnt++; 256 w = 2 * PetscMin(1.0 - x, x); 257 wd = w / (cnt + 1); 258 259 PetscCall(PetscSNPrintf(str, 32, "Schur fact. %s", PCFieldSplitSchurFactTypes[jac->schurfactorization])); 260 PetscCall(PetscDrawStringBoxed(draw, x, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h)); 261 y -= h; 262 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_USER && !jac->schur_user) { 263 PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[PC_FIELDSPLIT_SCHUR_PRE_A11])); 264 } else { 265 PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[jac->schurpre])); 266 } 267 PetscCall(PetscDrawStringBoxed(draw, x + wd * (cnt - 1) / 2.0, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h)); 268 y -= h; 269 x = x - wd * (cnt - 1) / 2.0; 270 271 PetscCall(PetscDrawPushCurrentPoint(draw, x, y)); 272 PetscCall(KSPView(jac->head->ksp, viewer)); 273 PetscCall(PetscDrawPopCurrentPoint(draw)); 274 if (jac->kspupper != jac->head->ksp) { 275 x += wd; 276 PetscCall(PetscDrawPushCurrentPoint(draw, x, y)); 277 PetscCall(KSPView(jac->kspupper, viewer)); 278 PetscCall(PetscDrawPopCurrentPoint(draw)); 279 } 280 x += wd; 281 PetscCall(PetscDrawPushCurrentPoint(draw, x, y)); 282 PetscCall(KSPView(jac->kspschur, viewer)); 283 PetscCall(PetscDrawPopCurrentPoint(draw)); 284 } 285 PetscFunctionReturn(PETSC_SUCCESS); 286 } 287 288 static PetscErrorCode PCView_FieldSplit_GKB(PC pc, PetscViewer viewer) 289 { 290 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 291 PetscBool iascii, isdraw; 292 PetscInt i, j; 293 PC_FieldSplitLink ilink = jac->head; 294 295 PetscFunctionBegin; 296 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii)); 297 PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw)); 298 if (iascii) { 299 if (jac->bs > 0) { 300 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs)); 301 } else { 302 PetscCall(PetscViewerASCIIPrintf(viewer, " FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits)); 303 } 304 if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for blocks\n")); 305 if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for diagonal blocks\n")); 306 if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, " using Amat (not Pmat) as operator for off-diagonal blocks\n")); 307 308 PetscCall(PetscViewerASCIIPrintf(viewer, " Stopping tolerance=%.1e, delay in error estimate=%" PetscInt_FMT ", maximum iterations=%" PetscInt_FMT "\n", (double)jac->gkbtol, jac->gkbdelay, jac->gkbmaxit)); 309 PetscCall(PetscViewerASCIIPrintf(viewer, " Solver info for H = A00 + nu*A01*A01' matrix:\n")); 310 PetscCall(PetscViewerASCIIPushTab(viewer)); 311 312 if (ilink->fields) { 313 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Fields ")); 314 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE)); 315 for (j = 0; j < ilink->nfields; j++) { 316 if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ",")); 317 PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j])); 318 } 319 PetscCall(PetscViewerASCIIPrintf(viewer, "\n")); 320 PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE)); 321 } else { 322 PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Defined by IS\n")); 323 } 324 PetscCall(KSPView(ilink->ksp, viewer)); 325 326 PetscCall(PetscViewerASCIIPopTab(viewer)); 327 } 328 329 if (isdraw) { 330 PetscDraw draw; 331 PetscReal x, y, w, wd; 332 333 PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw)); 334 PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y)); 335 w = 2 * PetscMin(1.0 - x, x); 336 wd = w / (jac->nsplits + 1); 337 x = x - wd * (jac->nsplits - 1) / 2.0; 338 for (i = 0; i < jac->nsplits; i++) { 339 PetscCall(PetscDrawPushCurrentPoint(draw, x, y)); 340 PetscCall(KSPView(ilink->ksp, viewer)); 341 PetscCall(PetscDrawPopCurrentPoint(draw)); 342 x += wd; 343 ilink = ilink->next; 344 } 345 } 346 PetscFunctionReturn(PETSC_SUCCESS); 347 } 348 349 /* Precondition: jac->bs is set to a meaningful value or MATNEST */ 350 static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc) 351 { 352 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 353 PetscInt bs, i, nfields, *ifields, nfields_col, *ifields_col; 354 PetscBool flg, flg_col, mnest; 355 char optionname[128], splitname[8], optionname_col[128]; 356 357 PetscFunctionBegin; 358 PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &mnest)); 359 if (mnest) { 360 PetscCall(MatNestGetSize(pc->pmat, &bs, NULL)); 361 } else { 362 bs = jac->bs; 363 } 364 PetscCall(PetscMalloc2(bs, &ifields, bs, &ifields_col)); 365 for (i = 0, flg = PETSC_TRUE;; i++) { 366 PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i)); 367 PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i)); 368 PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i)); 369 nfields = bs; 370 nfields_col = bs; 371 PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg)); 372 PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col)); 373 if (!flg) break; 374 else if (flg && !flg_col) { 375 PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields"); 376 PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields)); 377 } else { 378 PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields"); 379 PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match"); 380 PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col)); 381 } 382 } 383 if (i > 0) { 384 /* Makes command-line setting of splits take precedence over setting them in code. 385 Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would 386 create new splits, which would probably not be what the user wanted. */ 387 jac->splitdefined = PETSC_TRUE; 388 } 389 PetscCall(PetscFree2(ifields, ifields_col)); 390 PetscFunctionReturn(PETSC_SUCCESS); 391 } 392 393 static PetscErrorCode PCFieldSplitSetDefaults(PC pc) 394 { 395 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 396 PC_FieldSplitLink ilink = jac->head; 397 PetscBool fieldsplit_default = PETSC_FALSE, coupling = PETSC_FALSE; 398 PetscInt i; 399 400 PetscFunctionBegin; 401 /* 402 Kinda messy, but at least this now uses DMCreateFieldDecomposition(). 403 Should probably be rewritten. 404 */ 405 if (!ilink) { 406 PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_detect_coupling", &coupling, NULL)); 407 if (pc->dm && jac->dm_splits && !jac->detect && !coupling) { 408 PetscInt numFields, f, i, j; 409 char **fieldNames; 410 IS *fields; 411 DM *dms; 412 DM subdm[128]; 413 PetscBool flg; 414 415 PetscCall(DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms)); 416 /* Allow the user to prescribe the splits */ 417 for (i = 0, flg = PETSC_TRUE;; i++) { 418 PetscInt ifields[128]; 419 IS compField; 420 char optionname[128], splitname[8]; 421 PetscInt nfields = numFields; 422 423 PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i)); 424 PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg)); 425 if (!flg) break; 426 PetscCheck(numFields <= 128, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot currently support %" PetscInt_FMT " > 128 fields", numFields); 427 PetscCall(DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i])); 428 if (nfields == 1) { 429 PetscCall(PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField)); 430 } else { 431 PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i)); 432 PetscCall(PCFieldSplitSetIS(pc, splitname, compField)); 433 } 434 PetscCall(ISDestroy(&compField)); 435 for (j = 0; j < nfields; ++j) { 436 f = ifields[j]; 437 PetscCall(PetscFree(fieldNames[f])); 438 PetscCall(ISDestroy(&fields[f])); 439 } 440 } 441 if (i == 0) { 442 for (f = 0; f < numFields; ++f) { 443 PetscCall(PCFieldSplitSetIS(pc, fieldNames[f], fields[f])); 444 PetscCall(PetscFree(fieldNames[f])); 445 PetscCall(ISDestroy(&fields[f])); 446 } 447 } else { 448 for (j = 0; j < numFields; j++) PetscCall(DMDestroy(dms + j)); 449 PetscCall(PetscFree(dms)); 450 PetscCall(PetscMalloc1(i, &dms)); 451 for (j = 0; j < i; ++j) dms[j] = subdm[j]; 452 } 453 PetscCall(PetscFree(fieldNames)); 454 PetscCall(PetscFree(fields)); 455 if (dms) { 456 PetscCall(PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n")); 457 for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) { 458 const char *prefix; 459 PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ilink->ksp, &prefix)); 460 PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dms[i], prefix)); 461 PetscCall(KSPSetDM(ilink->ksp, dms[i])); 462 PetscCall(KSPSetDMActive(ilink->ksp, PETSC_FALSE)); 463 PetscCall(PetscObjectIncrementTabLevel((PetscObject)dms[i], (PetscObject)ilink->ksp, 0)); 464 PetscCall(DMDestroy(&dms[i])); 465 } 466 PetscCall(PetscFree(dms)); 467 } 468 } else { 469 if (jac->bs <= 0) { 470 if (pc->pmat) { 471 PetscCall(MatGetBlockSize(pc->pmat, &jac->bs)); 472 } else jac->bs = 1; 473 } 474 475 if (jac->detect) { 476 IS zerodiags, rest; 477 PetscInt nmin, nmax; 478 479 PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax)); 480 if (jac->diag_use_amat) { 481 PetscCall(MatFindZeroDiagonals(pc->mat, &zerodiags)); 482 } else { 483 PetscCall(MatFindZeroDiagonals(pc->pmat, &zerodiags)); 484 } 485 PetscCall(ISComplement(zerodiags, nmin, nmax, &rest)); 486 PetscCall(PCFieldSplitSetIS(pc, "0", rest)); 487 PetscCall(PCFieldSplitSetIS(pc, "1", zerodiags)); 488 PetscCall(ISDestroy(&zerodiags)); 489 PetscCall(ISDestroy(&rest)); 490 } else if (coupling) { 491 IS coupling, rest; 492 PetscInt nmin, nmax; 493 494 PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax)); 495 if (jac->offdiag_use_amat) { 496 PetscCall(MatFindOffBlockDiagonalEntries(pc->mat, &coupling)); 497 } else { 498 PetscCall(MatFindOffBlockDiagonalEntries(pc->pmat, &coupling)); 499 } 500 PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc->mat), nmax - nmin, nmin, 1, &rest)); 501 PetscCall(ISSetIdentity(rest)); 502 PetscCall(PCFieldSplitSetIS(pc, "0", rest)); 503 PetscCall(PCFieldSplitSetIS(pc, "1", coupling)); 504 PetscCall(ISDestroy(&coupling)); 505 PetscCall(ISDestroy(&rest)); 506 } else { 507 PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_default", &fieldsplit_default, NULL)); 508 if (!fieldsplit_default) { 509 /* Allow user to set fields from command line, if bs was known at the time of PCSetFromOptions_FieldSplit() 510 then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */ 511 PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc)); 512 if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n")); 513 } 514 if ((fieldsplit_default || !jac->splitdefined) && !jac->isrestrict) { 515 Mat M = pc->pmat; 516 PetscBool isnest; 517 PetscInt nf; 518 519 PetscCall(PetscInfo(pc, "Using default splitting of fields\n")); 520 PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &isnest)); 521 if (!isnest) { 522 M = pc->mat; 523 PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &isnest)); 524 } 525 if (!isnest) nf = jac->bs; 526 else PetscCall(MatNestGetSize(M, &nf, NULL)); 527 for (i = 0; i < nf; i++) { 528 char splitname[8]; 529 530 PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i)); 531 PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i)); 532 } 533 jac->defaultsplit = PETSC_TRUE; 534 } 535 } 536 } 537 } else if (jac->nsplits == 1) { 538 IS is2; 539 PetscInt nmin, nmax; 540 541 PetscCheck(ilink->is, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Must provide at least two sets of fields to PCFieldSplit()"); 542 PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax)); 543 PetscCall(ISComplement(ilink->is, nmin, nmax, &is2)); 544 PetscCall(PCFieldSplitSetIS(pc, "1", is2)); 545 PetscCall(ISDestroy(&is2)); 546 } 547 548 PetscCheck(jac->nsplits >= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unhandled case, must have at least two fields, not %" PetscInt_FMT, jac->nsplits); 549 PetscFunctionReturn(PETSC_SUCCESS); 550 } 551 552 static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu) 553 { 554 Mat BT, T; 555 PetscReal nrmT, nrmB; 556 557 PetscFunctionBegin; 558 PetscCall(MatHermitianTranspose(C, MAT_INITIAL_MATRIX, &T)); /* Test if augmented matrix is symmetric */ 559 PetscCall(MatAXPY(T, -1.0, B, DIFFERENT_NONZERO_PATTERN)); 560 PetscCall(MatNorm(T, NORM_1, &nrmT)); 561 PetscCall(MatNorm(B, NORM_1, &nrmB)); 562 PetscCheck(nrmB <= 0 || nrmT / nrmB < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix is not symmetric/hermitian, GKB is not applicable."); 563 564 /* Compute augmented Lagrangian matrix H = A00 + nu*A01*A01'. This corresponds to */ 565 /* setting N := 1/nu*I in [Ar13]. */ 566 PetscCall(MatHermitianTranspose(B, MAT_INITIAL_MATRIX, &BT)); 567 PetscCall(MatMatMult(B, BT, MAT_INITIAL_MATRIX, PETSC_CURRENT, H)); /* H = A01*A01' */ 568 PetscCall(MatAYPX(*H, gkbnu, A, DIFFERENT_NONZERO_PATTERN)); /* H = A00 + nu*A01*A01' */ 569 570 PetscCall(MatDestroy(&BT)); 571 PetscCall(MatDestroy(&T)); 572 PetscFunctionReturn(PETSC_SUCCESS); 573 } 574 575 PETSC_EXTERN PetscErrorCode PetscOptionsFindPairPrefix_Private(PetscOptions, const char pre[], const char name[], const char *option[], const char *value[], PetscBool *flg); 576 577 static PetscErrorCode PCSetUp_FieldSplit(PC pc) 578 { 579 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 580 PC_FieldSplitLink ilink; 581 PetscInt i, nsplit; 582 PetscBool sorted, sorted_col, matnest = PETSC_FALSE; 583 584 PetscFunctionBegin; 585 pc->failedreason = PC_NOERROR; 586 PetscCall(PCFieldSplitSetDefaults(pc)); 587 nsplit = jac->nsplits; 588 ilink = jac->head; 589 if (pc->pmat) PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest)); 590 591 /* get the matrices for each split */ 592 if (!jac->issetup) { 593 PetscInt rstart, rend, nslots, bs; 594 595 jac->issetup = PETSC_TRUE; 596 597 /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */ 598 if (jac->defaultsplit || !ilink->is) { 599 if (jac->bs <= 0) jac->bs = nsplit; 600 } 601 602 /* MatCreateSubMatrix() for [S]BAIJ matrices can only work if the indices include entire blocks of the matrix */ 603 PetscCall(MatGetBlockSize(pc->pmat, &bs)); 604 if (bs > 1 && (jac->bs <= bs || jac->bs % bs)) { 605 PetscBool blk; 606 607 PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL)); 608 PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes"); 609 } 610 611 if (!matnest) { /* use the matrix blocksize and stride IS to determine the index sets that define the submatrices */ 612 bs = jac->bs; 613 PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend)); 614 nslots = (rend - rstart) / bs; 615 for (i = 0; i < nsplit; i++) { 616 if (jac->defaultsplit) { 617 PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is)); 618 PetscCall(ISDuplicate(ilink->is, &ilink->is_col)); 619 } else if (!ilink->is) { 620 if (ilink->nfields > 1) { 621 PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col; 622 623 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 } else { /* use the IS that define the MATNEST to determine the index sets that define the submatrices */ 646 IS *rowis, *colis, *ises = NULL; 647 PetscInt mis, nis; 648 649 PetscCall(MatNestGetSize(pc->pmat, &mis, &nis)); 650 PetscCall(PetscMalloc2(mis, &rowis, nis, &colis)); 651 PetscCall(MatNestGetISs(pc->pmat, rowis, colis)); 652 if (!jac->defaultsplit) PetscCall(PetscMalloc1(mis, &ises)); 653 654 for (i = 0; i < nsplit; i++) { 655 if (jac->defaultsplit) { 656 PetscCall(ISDuplicate(rowis[i], &ilink->is)); 657 PetscCall(ISDuplicate(ilink->is, &ilink->is_col)); 658 } else if (!ilink->is) { 659 if (ilink->nfields > 1) { 660 for (PetscInt j = 0; j < ilink->nfields; j++) ises[j] = rowis[ilink->fields[j]]; 661 PetscCall(ISConcatenate(PetscObjectComm((PetscObject)pc), ilink->nfields, ises, &ilink->is)); 662 } else { 663 PetscCall(ISDuplicate(rowis[ilink->fields[0]], &ilink->is)); 664 } 665 PetscCall(ISDuplicate(ilink->is, &ilink->is_col)); 666 } 667 ilink = ilink->next; 668 } 669 PetscCall(PetscFree2(rowis, colis)); 670 PetscCall(PetscFree(ises)); 671 } 672 } 673 674 ilink = jac->head; 675 if (!jac->pmat) { 676 Vec xtmp; 677 678 PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL)); 679 PetscCall(PetscMalloc1(nsplit, &jac->pmat)); 680 PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y)); 681 for (i = 0; i < nsplit; i++) { 682 MatNullSpace sp; 683 684 /* Check for preconditioning matrix attached to IS */ 685 PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i])); 686 if (jac->pmat[i]) { 687 PetscCall(PetscObjectReference((PetscObject)jac->pmat[i])); 688 if (jac->type == PC_COMPOSITE_SCHUR) { 689 jac->schur_user = jac->pmat[i]; 690 691 PetscCall(PetscObjectReference((PetscObject)jac->schur_user)); 692 } 693 } else { 694 const char *prefix; 695 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i])); 696 PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix)); 697 if (!prefix) { 698 PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix)); 699 PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix)); 700 } 701 PetscCall(MatSetFromOptions(jac->pmat[i])); 702 PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view")); 703 } 704 /* create work vectors for each split */ 705 PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i])); 706 ilink->x = jac->x[i]; 707 ilink->y = jac->y[i]; 708 ilink->z = NULL; 709 /* compute scatter contexts needed by multiplicative versions and non-default splits */ 710 PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx)); 711 PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp)); 712 if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp)); 713 ilink = ilink->next; 714 } 715 PetscCall(VecDestroy(&xtmp)); 716 } else { 717 MatReuse scall; 718 MatNullSpace *nullsp = NULL; 719 720 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 721 PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp)); 722 for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i])); 723 scall = MAT_INITIAL_MATRIX; 724 } else scall = MAT_REUSE_MATRIX; 725 726 for (i = 0; i < nsplit; i++) { 727 Mat pmat; 728 729 /* Check for preconditioning matrix attached to IS */ 730 PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat)); 731 if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i])); 732 ilink = ilink->next; 733 } 734 if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp)); 735 } 736 if (jac->diag_use_amat) { 737 ilink = jac->head; 738 if (!jac->mat) { 739 PetscCall(PetscMalloc1(nsplit, &jac->mat)); 740 for (i = 0; i < nsplit; i++) { 741 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i])); 742 ilink = ilink->next; 743 } 744 } else { 745 MatReuse scall; 746 MatNullSpace *nullsp = NULL; 747 748 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 749 PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp)); 750 for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i])); 751 scall = MAT_INITIAL_MATRIX; 752 } else scall = MAT_REUSE_MATRIX; 753 754 for (i = 0; i < nsplit; i++) { 755 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i])); 756 ilink = ilink->next; 757 } 758 if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp)); 759 } 760 } else { 761 jac->mat = jac->pmat; 762 } 763 764 /* Check for null space attached to IS */ 765 ilink = jac->head; 766 for (i = 0; i < nsplit; i++) { 767 MatNullSpace sp; 768 769 PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp)); 770 if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp)); 771 ilink = ilink->next; 772 } 773 774 if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) { 775 /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */ 776 /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */ 777 ilink = jac->head; 778 if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) { 779 /* 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 */ 780 if (!jac->Afield) { 781 PetscCall(PetscCalloc1(nsplit, &jac->Afield)); 782 if (jac->offdiag_use_amat) { 783 PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1])); 784 } else { 785 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1])); 786 } 787 } else { 788 MatReuse scall; 789 790 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 791 PetscCall(MatDestroy(&jac->Afield[1])); 792 scall = MAT_INITIAL_MATRIX; 793 } else scall = MAT_REUSE_MATRIX; 794 795 if (jac->offdiag_use_amat) { 796 PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1])); 797 } else { 798 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1])); 799 } 800 } 801 } else { 802 if (!jac->Afield) { 803 PetscCall(PetscMalloc1(nsplit, &jac->Afield)); 804 for (i = 0; i < nsplit; i++) { 805 if (jac->offdiag_use_amat) { 806 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i])); 807 } else { 808 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i])); 809 } 810 ilink = ilink->next; 811 } 812 } else { 813 MatReuse scall; 814 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 815 for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i])); 816 scall = MAT_INITIAL_MATRIX; 817 } else scall = MAT_REUSE_MATRIX; 818 819 for (i = 0; i < nsplit; i++) { 820 if (jac->offdiag_use_amat) { 821 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i])); 822 } else { 823 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i])); 824 } 825 ilink = ilink->next; 826 } 827 } 828 } 829 } 830 831 if (jac->type == PC_COMPOSITE_SCHUR) { 832 IS ccis; 833 PetscBool isset, isspd; 834 PetscInt rstart, rend; 835 char lscname[256]; 836 PetscObject LSC_L; 837 PetscBool set, flg; 838 839 PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields"); 840 841 /* If pc->mat is SPD, don't scale by -1 the Schur complement */ 842 if (jac->schurscale == (PetscScalar)-1.0) { 843 PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd)); 844 jac->schurscale = (isset && isspd) ? 1.0 : -1.0; 845 } 846 847 /* When extracting off-diagonal submatrices, we take complements from this range */ 848 PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend)); 849 PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, "")); 850 851 if (jac->schur) { 852 KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper; 853 MatReuse scall; 854 855 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 856 scall = MAT_INITIAL_MATRIX; 857 PetscCall(MatDestroy(&jac->B)); 858 PetscCall(MatDestroy(&jac->C)); 859 } else scall = MAT_REUSE_MATRIX; 860 861 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 862 ilink = jac->head; 863 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 864 if (jac->offdiag_use_amat) { 865 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B)); 866 } else { 867 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B)); 868 } 869 PetscCall(ISDestroy(&ccis)); 870 if (!flg) { 871 ilink = ilink->next; 872 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 873 if (jac->offdiag_use_amat) { 874 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C)); 875 } else { 876 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C)); 877 } 878 PetscCall(ISDestroy(&ccis)); 879 } else { 880 PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg)); 881 if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C)); 882 else PetscCall(MatCreateTranspose(jac->B, &jac->C)); 883 } 884 PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1])); 885 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) { 886 PetscCall(MatDestroy(&jac->schurp)); 887 PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp)); 888 } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) { 889 PetscCall(MatDestroy(&jac->schur_user)); 890 if (jac->kspupper == jac->head->ksp) { 891 Mat AinvB; 892 893 PetscCall(MatCreate(PetscObjectComm((PetscObject)jac->schur), &AinvB)); 894 PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)AinvB)); 895 PetscCall(MatDestroy(&AinvB)); 896 } 897 PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 898 } 899 if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0])); 900 if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0])); 901 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac))); 902 } else { 903 const char *Dprefix; 904 char schurprefix[256], schurmatprefix[256]; 905 char schurtestoption[256]; 906 MatNullSpace sp; 907 KSP kspt; 908 909 /* extract the A01 and A10 matrices */ 910 ilink = jac->head; 911 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 912 if (jac->offdiag_use_amat) { 913 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 914 } else { 915 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 916 } 917 PetscCall(ISDestroy(&ccis)); 918 ilink = ilink->next; 919 if (!flg) { 920 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 921 if (jac->offdiag_use_amat) { 922 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 923 } else { 924 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 925 } 926 PetscCall(ISDestroy(&ccis)); 927 } else { 928 PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg)); 929 if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C)); 930 else PetscCall(MatCreateTranspose(jac->B, &jac->C)); 931 } 932 /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */ 933 PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur)); 934 PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT)); 935 PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1])); 936 PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 937 PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix)); 938 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt)); 939 PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix)); 940 941 /* Note: this is not true in general */ 942 PetscCall(MatGetNullSpace(jac->mat[1], &sp)); 943 if (sp) PetscCall(MatSetNullSpace(jac->schur, sp)); 944 945 PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname)); 946 PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg)); 947 if (flg) { 948 DM dmInner; 949 KSP kspInner; 950 PC pcInner; 951 952 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 953 PetscCall(KSPReset(kspInner)); 954 PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0])); 955 PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 956 /* Indent this deeper to emphasize the "inner" nature of this solver. */ 957 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2)); 958 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2)); 959 PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix)); 960 961 /* Set DM for new solver */ 962 PetscCall(KSPGetDM(jac->head->ksp, &dmInner)); 963 PetscCall(KSPSetDM(kspInner, dmInner)); 964 PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE)); 965 966 /* Defaults to PCKSP as preconditioner */ 967 PetscCall(KSPGetPC(kspInner, &pcInner)); 968 PetscCall(PCSetType(pcInner, PCKSP)); 969 PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp)); 970 } else { 971 /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or 972 * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact, 973 * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for 974 * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make 975 * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used 976 * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */ 977 PetscCall(KSPSetType(jac->head->ksp, KSPGMRES)); 978 PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp)); 979 } 980 PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0])); 981 PetscCall(KSPSetFromOptions(jac->head->ksp)); 982 PetscCall(MatSetFromOptions(jac->schur)); 983 984 PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg)); 985 if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */ 986 KSP kspInner; 987 PC pcInner; 988 989 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 990 PetscCall(KSPGetPC(kspInner, &pcInner)); 991 PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg)); 992 if (flg) { 993 KSP ksp; 994 995 PetscCall(PCKSPGetKSP(pcInner, &ksp)); 996 if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE)); 997 } 998 } 999 PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname)); 1000 PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg)); 1001 if (flg) { 1002 DM dmInner; 1003 1004 PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 1005 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper)); 1006 PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel)); 1007 PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure)); 1008 PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix)); 1009 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1)); 1010 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1)); 1011 PetscCall(KSPGetDM(jac->head->ksp, &dmInner)); 1012 PetscCall(KSPSetDM(jac->kspupper, dmInner)); 1013 PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE)); 1014 PetscCall(KSPSetFromOptions(jac->kspupper)); 1015 PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0])); 1016 PetscCall(VecDuplicate(jac->head->x, &jac->head->z)); 1017 } else { 1018 jac->kspupper = jac->head->ksp; 1019 PetscCall(PetscObjectReference((PetscObject)jac->head->ksp)); 1020 } 1021 1022 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp)); 1023 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur)); 1024 PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel)); 1025 PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure)); 1026 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1)); 1027 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) { 1028 PC pcschur; 1029 PetscCall(KSPGetPC(jac->kspschur, &pcschur)); 1030 PetscCall(PCSetType(pcschur, PCNONE)); 1031 /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */ 1032 } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) { 1033 if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && jac->kspupper == jac->head->ksp) { 1034 Mat AinvB; 1035 1036 PetscCall(MatCreate(PetscObjectComm((PetscObject)jac->schur), &AinvB)); 1037 PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)AinvB)); 1038 PetscCall(MatDestroy(&AinvB)); 1039 } 1040 PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 1041 } 1042 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac))); 1043 PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix)); 1044 PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix)); 1045 /* propagate DM */ 1046 { 1047 DM sdm; 1048 PetscCall(KSPGetDM(jac->head->next->ksp, &sdm)); 1049 if (sdm) { 1050 PetscCall(KSPSetDM(jac->kspschur, sdm)); 1051 PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE)); 1052 } 1053 } 1054 /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */ 1055 /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */ 1056 PetscCall(KSPSetFromOptions(jac->kspschur)); 1057 } 1058 PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY)); 1059 PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY)); 1060 1061 /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */ 1062 PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname)); 1063 PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L)); 1064 if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L)); 1065 if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L)); 1066 PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname)); 1067 PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L)); 1068 if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L)); 1069 if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L)); 1070 } else if (jac->type == PC_COMPOSITE_GKB) { 1071 IS ccis; 1072 PetscInt rstart, rend; 1073 1074 PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields"); 1075 1076 ilink = jac->head; 1077 1078 /* When extracting off-diagonal submatrices, we take complements from this range */ 1079 PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend)); 1080 1081 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 1082 if (jac->offdiag_use_amat) { 1083 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 1084 } else { 1085 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 1086 } 1087 PetscCall(ISDestroy(&ccis)); 1088 /* Create work vectors for GKB algorithm */ 1089 PetscCall(VecDuplicate(ilink->x, &jac->u)); 1090 PetscCall(VecDuplicate(ilink->x, &jac->Hu)); 1091 PetscCall(VecDuplicate(ilink->x, &jac->w2)); 1092 ilink = ilink->next; 1093 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 1094 if (jac->offdiag_use_amat) { 1095 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 1096 } else { 1097 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 1098 } 1099 PetscCall(ISDestroy(&ccis)); 1100 /* Create work vectors for GKB algorithm */ 1101 PetscCall(VecDuplicate(ilink->x, &jac->v)); 1102 PetscCall(VecDuplicate(ilink->x, &jac->d)); 1103 PetscCall(VecDuplicate(ilink->x, &jac->w1)); 1104 PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu)); 1105 PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz)); 1106 1107 ilink = jac->head; 1108 PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H)); 1109 if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp)); 1110 /* Create gkb_monitor context */ 1111 if (jac->gkbmonitor) { 1112 PetscInt tablevel; 1113 PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer)); 1114 PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII)); 1115 PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel)); 1116 PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel)); 1117 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1)); 1118 } 1119 } else { 1120 /* set up the individual splits' PCs */ 1121 i = 0; 1122 ilink = jac->head; 1123 while (ilink) { 1124 PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i])); 1125 /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */ 1126 if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp)); 1127 i++; 1128 ilink = ilink->next; 1129 } 1130 } 1131 1132 /* Set coordinates to the sub PC objects whenever these are set */ 1133 if (jac->coordinates_set) { 1134 PC pc_coords; 1135 if (jac->type == PC_COMPOSITE_SCHUR) { 1136 // Head is first block. 1137 PetscCall(KSPGetPC(jac->head->ksp, &pc_coords)); 1138 PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords)); 1139 // Second one is Schur block, but its KSP object is in kspschur. 1140 PetscCall(KSPGetPC(jac->kspschur, &pc_coords)); 1141 PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords)); 1142 } else if (jac->type == PC_COMPOSITE_GKB) { 1143 PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n")); 1144 } else { 1145 ilink = jac->head; 1146 while (ilink) { 1147 PetscCall(KSPGetPC(ilink->ksp, &pc_coords)); 1148 PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords)); 1149 ilink = ilink->next; 1150 } 1151 } 1152 } 1153 1154 jac->suboptionsset = PETSC_TRUE; 1155 PetscFunctionReturn(PETSC_SUCCESS); 1156 } 1157 1158 #define FieldSplitSplitSolveAdd(ilink, xx, yy) \ 1159 ((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) || \ 1160 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) || \ 1161 VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE))) 1162 1163 static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc) 1164 { 1165 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1166 PC_FieldSplitLink ilinkA = jac->head; 1167 KSP kspA = ilinkA->ksp, kspUpper = jac->kspupper; 1168 1169 PetscFunctionBegin; 1170 if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) { 1171 PetscCall(KSPSetUp(kspUpper)); 1172 PetscCall(KSPSetUpOnBlocks(kspUpper)); 1173 } 1174 PetscCall(KSPSetUp(kspA)); 1175 PetscCall(KSPSetUpOnBlocks(kspA)); 1176 if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) { 1177 PetscCall(KSPSetUp(jac->kspschur)); 1178 PetscCall(KSPSetUpOnBlocks(jac->kspschur)); 1179 } else if (kspUpper == kspA) { 1180 Mat AinvB, A; 1181 PetscInt m, M, N; 1182 1183 PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB)); 1184 if (AinvB) { 1185 PetscCall(MatGetSize(AinvB, NULL, &N)); 1186 if (N == -1) { // first time PCSetUpOnBlocks_FieldSplit_Schur() is called 1187 VecType vtype; 1188 PetscMemType mtype; 1189 PetscScalar *array; 1190 1191 PetscCall(MatGetSize(jac->B, &M, &N)); 1192 PetscCall(MatGetLocalSize(jac->B, &m, NULL)); 1193 PetscCall(MatGetVecType(jac->B, &vtype)); 1194 PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype)); 1195 PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array)); 1196 if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array)); 1197 #if PetscDefined(HAVE_CUDA) 1198 else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1))); 1199 #endif 1200 #if PetscDefined(HAVE_HIP) 1201 else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1))); 1202 #endif 1203 PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)jac->schur), vtype, m, PETSC_DECIDE, M, N + 1, -1, array, &A)); // number of columns of the Schur complement plus one 1204 PetscCall(MatHeaderReplace(AinvB, &A)); 1205 } 1206 } 1207 } 1208 PetscFunctionReturn(PETSC_SUCCESS); 1209 } 1210 1211 static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc) 1212 { 1213 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1214 PC_FieldSplitLink ilink = jac->head; 1215 1216 PetscFunctionBegin; 1217 while (ilink) { 1218 PetscCall(KSPSetUp(ilink->ksp)); 1219 PetscCall(KSPSetUpOnBlocks(ilink->ksp)); 1220 ilink = ilink->next; 1221 } 1222 PetscFunctionReturn(PETSC_SUCCESS); 1223 } 1224 1225 static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc) 1226 { 1227 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1228 PC_FieldSplitLink ilinkA = jac->head; 1229 KSP ksp = ilinkA->ksp; 1230 1231 PetscFunctionBegin; 1232 PetscCall(KSPSetUp(ksp)); 1233 PetscCall(KSPSetUpOnBlocks(ksp)); 1234 PetscFunctionReturn(PETSC_SUCCESS); 1235 } 1236 1237 static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y) 1238 { 1239 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1240 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1241 KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper; 1242 Mat AinvB = NULL; 1243 PetscInt N, P; 1244 1245 PetscFunctionBegin; 1246 switch (jac->schurfactorization) { 1247 case PC_FIELDSPLIT_SCHUR_FACT_DIAG: 1248 /* [A00 0; 0 -S], positive definite, suitable for MINRES */ 1249 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1250 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1251 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1252 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1253 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1254 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1255 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1256 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1257 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1258 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1259 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1260 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1261 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1262 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1263 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1264 PetscCall(VecScale(ilinkD->y, jac->schurscale)); 1265 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1266 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1267 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1268 break; 1269 case PC_FIELDSPLIT_SCHUR_FACT_LOWER: 1270 /* [A00 0; A10 S], suitable for left preconditioning */ 1271 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1272 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1273 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1274 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1275 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1276 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1277 PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x)); 1278 PetscCall(VecScale(ilinkD->x, -1.)); 1279 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1280 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1281 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1282 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1283 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1284 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1285 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1286 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1287 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1288 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1289 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1290 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1291 break; 1292 case PC_FIELDSPLIT_SCHUR_FACT_UPPER: 1293 /* [A00 A01; 0 S], suitable for right preconditioning */ 1294 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1295 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1296 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1297 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1298 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1299 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1300 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1301 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1302 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x)); 1303 PetscCall(VecScale(ilinkA->x, -1.)); 1304 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1305 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1306 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1307 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1308 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1309 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1310 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1311 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1312 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1313 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1314 break; 1315 case PC_FIELDSPLIT_SCHUR_FACT_FULL: 1316 /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */ 1317 PetscCall(MatGetSize(jac->B, NULL, &P)); 1318 N = P; 1319 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1320 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1321 PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL)); 1322 if (kspUpper == kspA) { 1323 PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB)); 1324 if (AinvB) { 1325 PetscCall(MatGetSize(AinvB, NULL, &N)); 1326 if (N > P) { // first time PCApply_FieldSplit_Schur() is called 1327 PetscMemType mtype; 1328 Vec c = NULL; 1329 PetscScalar *array; 1330 PetscInt m, M; 1331 1332 PetscCall(MatGetSize(jac->B, &M, NULL)); 1333 PetscCall(MatGetLocalSize(jac->B, &m, NULL)); 1334 PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype)); 1335 if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1336 #if PetscDefined(HAVE_CUDA) 1337 else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1338 #endif 1339 #if PetscDefined(HAVE_HIP) 1340 else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1341 #endif 1342 PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array)); 1343 PetscCall(VecCopy(ilinkA->x, c)); 1344 PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 1345 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user)); 1346 PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat 1347 PetscCall(VecDestroy(&c)); 1348 } 1349 } 1350 } 1351 if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y)); 1352 PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y)); 1353 PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL)); 1354 PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x)); 1355 PetscCall(VecScale(ilinkD->x, -1.0)); 1356 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1357 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1358 1359 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1360 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1361 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1362 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1363 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1364 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1365 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1366 1367 if (kspUpper == kspA) { 1368 if (!AinvB) { 1369 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y)); 1370 PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y)); 1371 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1372 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1373 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1374 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1375 } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y)); 1376 } else { 1377 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1378 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1379 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1380 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x)); 1381 PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL)); 1382 PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z)); 1383 PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z)); 1384 PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL)); 1385 PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z)); 1386 } 1387 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1388 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1389 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1390 } 1391 PetscFunctionReturn(PETSC_SUCCESS); 1392 } 1393 1394 static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y) 1395 { 1396 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1397 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1398 KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper; 1399 1400 PetscFunctionBegin; 1401 switch (jac->schurfactorization) { 1402 case PC_FIELDSPLIT_SCHUR_FACT_DIAG: 1403 /* [A00 0; 0 -S], positive definite, suitable for MINRES */ 1404 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1405 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1406 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1407 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1408 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1409 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1410 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1411 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1412 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1413 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1414 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1415 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1416 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1417 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1418 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1419 PetscCall(VecScale(ilinkD->y, jac->schurscale)); 1420 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1421 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1422 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1423 break; 1424 case PC_FIELDSPLIT_SCHUR_FACT_UPPER: 1425 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1426 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1427 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1428 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1429 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1430 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1431 PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x)); 1432 PetscCall(VecScale(ilinkD->x, -1.)); 1433 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1434 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1435 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1436 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1437 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1438 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1439 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1440 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1441 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1442 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1443 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1444 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1445 break; 1446 case PC_FIELDSPLIT_SCHUR_FACT_LOWER: 1447 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1448 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1449 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1450 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1451 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1452 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1453 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1454 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1455 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x)); 1456 PetscCall(VecScale(ilinkA->x, -1.)); 1457 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1458 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1459 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1460 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1461 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1462 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1463 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1464 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1465 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1466 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1467 break; 1468 case PC_FIELDSPLIT_SCHUR_FACT_FULL: 1469 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1470 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1471 PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL)); 1472 PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y)); 1473 PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y)); 1474 PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL)); 1475 PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x)); 1476 PetscCall(VecScale(ilinkD->x, -1.0)); 1477 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1478 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1479 1480 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1481 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1482 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1483 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1484 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1485 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1486 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1487 1488 if (kspLower == kspA) { 1489 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y)); 1490 PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y)); 1491 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1492 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1493 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1494 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1495 } else { 1496 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1497 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1498 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1499 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x)); 1500 PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL)); 1501 PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z)); 1502 PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z)); 1503 PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL)); 1504 PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z)); 1505 } 1506 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1507 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1508 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1509 } 1510 PetscFunctionReturn(PETSC_SUCCESS); 1511 } 1512 1513 static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y) 1514 { 1515 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1516 PC_FieldSplitLink ilink = jac->head; 1517 PetscInt cnt, bs; 1518 1519 PetscFunctionBegin; 1520 if (jac->type == PC_COMPOSITE_ADDITIVE) { 1521 PetscBool matnest; 1522 1523 PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest)); 1524 if (jac->defaultsplit && !matnest) { 1525 PetscCall(VecGetBlockSize(x, &bs)); 1526 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); 1527 PetscCall(VecGetBlockSize(y, &bs)); 1528 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); 1529 PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES)); 1530 while (ilink) { 1531 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1532 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1533 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1534 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1535 ilink = ilink->next; 1536 } 1537 PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES)); 1538 } else { 1539 PetscCall(VecSet(y, 0.0)); 1540 while (ilink) { 1541 PetscCall(FieldSplitSplitSolveAdd(ilink, x, y)); 1542 ilink = ilink->next; 1543 } 1544 } 1545 } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) { 1546 PetscCall(VecSet(y, 0.0)); 1547 /* solve on first block for first block variables */ 1548 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD)); 1549 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD)); 1550 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1551 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1552 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1553 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1554 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1555 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1556 1557 /* compute the residual only onto second block variables using first block variables */ 1558 PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x)); 1559 ilink = ilink->next; 1560 PetscCall(VecScale(ilink->x, -1.0)); 1561 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1562 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1563 1564 /* solve on second block variables */ 1565 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1566 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1567 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1568 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1569 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1570 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1571 } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1572 if (!jac->w1) { 1573 PetscCall(VecDuplicate(x, &jac->w1)); 1574 PetscCall(VecDuplicate(x, &jac->w2)); 1575 } 1576 PetscCall(VecSet(y, 0.0)); 1577 PetscCall(FieldSplitSplitSolveAdd(ilink, x, y)); 1578 cnt = 1; 1579 while (ilink->next) { 1580 ilink = ilink->next; 1581 /* compute the residual only over the part of the vector needed */ 1582 PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x)); 1583 PetscCall(VecScale(ilink->x, -1.0)); 1584 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1585 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1586 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1587 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1588 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1589 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1590 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1591 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1592 } 1593 if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1594 cnt -= 2; 1595 while (ilink->previous) { 1596 ilink = ilink->previous; 1597 /* compute the residual only over the part of the vector needed */ 1598 PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x)); 1599 PetscCall(VecScale(ilink->x, -1.0)); 1600 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1601 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1602 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1603 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1604 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1605 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1606 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1607 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1608 } 1609 } 1610 } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type); 1611 PetscFunctionReturn(PETSC_SUCCESS); 1612 } 1613 1614 static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y) 1615 { 1616 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1617 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1618 KSP ksp = ilinkA->ksp; 1619 Vec u, v, Hu, d, work1, work2; 1620 PetscScalar alpha, z, nrmz2, *vecz; 1621 PetscReal lowbnd, nu, beta; 1622 PetscInt j, iterGKB; 1623 1624 PetscFunctionBegin; 1625 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1626 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1627 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1628 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1629 1630 u = jac->u; 1631 v = jac->v; 1632 Hu = jac->Hu; 1633 d = jac->d; 1634 work1 = jac->w1; 1635 work2 = jac->w2; 1636 vecz = jac->vecz; 1637 1638 /* Change RHS to comply with matrix regularization H = A + nu*B*B' */ 1639 /* Add q = q + nu*B*b */ 1640 if (jac->gkbnu) { 1641 nu = jac->gkbnu; 1642 PetscCall(VecScale(ilinkD->x, jac->gkbnu)); 1643 PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */ 1644 } else { 1645 /* Situation when no augmented Lagrangian is used. Then we set inner */ 1646 /* matrix N = I in [Ar13], and thus nu = 1. */ 1647 nu = 1; 1648 } 1649 1650 /* Transform rhs from [q,tilde{b}] to [0,b] */ 1651 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL)); 1652 PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y)); 1653 PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y)); 1654 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL)); 1655 PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1)); 1656 PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x */ 1657 1658 /* First step of algorithm */ 1659 PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/ 1660 KSPCheckDot(ksp, beta); 1661 beta = PetscSqrtReal(nu) * beta; 1662 PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c */ 1663 PetscCall(MatMult(jac->B, v, work2)); /* u = H^{-1}*B*v */ 1664 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL)); 1665 PetscCall(KSPSolve(ksp, work2, u)); 1666 PetscCall(KSPCheckSolve(ksp, pc, u)); 1667 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL)); 1668 PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */ 1669 PetscCall(VecDot(Hu, u, &alpha)); 1670 KSPCheckDot(ksp, alpha); 1671 PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite"); 1672 alpha = PetscSqrtReal(PetscAbsScalar(alpha)); 1673 PetscCall(VecScale(u, 1.0 / alpha)); 1674 PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c */ 1675 1676 z = beta / alpha; 1677 vecz[1] = z; 1678 1679 /* Computation of first iterate x(1) and p(1) */ 1680 PetscCall(VecAXPY(ilinkA->y, z, u)); 1681 PetscCall(VecCopy(d, ilinkD->y)); 1682 PetscCall(VecScale(ilinkD->y, -z)); 1683 1684 iterGKB = 1; 1685 lowbnd = 2 * jac->gkbtol; 1686 if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd)); 1687 1688 while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) { 1689 iterGKB += 1; 1690 PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */ 1691 PetscCall(VecAXPBY(v, nu, -alpha, work1)); 1692 PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v */ 1693 beta = beta / PetscSqrtReal(nu); 1694 PetscCall(VecScale(v, 1.0 / beta)); 1695 PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */ 1696 PetscCall(MatMult(jac->H, u, Hu)); 1697 PetscCall(VecAXPY(work2, -beta, Hu)); 1698 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL)); 1699 PetscCall(KSPSolve(ksp, work2, u)); 1700 PetscCall(KSPCheckSolve(ksp, pc, u)); 1701 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL)); 1702 PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */ 1703 PetscCall(VecDot(Hu, u, &alpha)); 1704 KSPCheckDot(ksp, alpha); 1705 PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite"); 1706 alpha = PetscSqrtReal(PetscAbsScalar(alpha)); 1707 PetscCall(VecScale(u, 1.0 / alpha)); 1708 1709 z = -beta / alpha * z; /* z <- beta/alpha*z */ 1710 vecz[0] = z; 1711 1712 /* Computation of new iterate x(i+1) and p(i+1) */ 1713 PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */ 1714 PetscCall(VecAXPY(ilinkA->y, z, u)); /* r = r + z*u */ 1715 PetscCall(VecAXPY(ilinkD->y, -z, d)); /* p = p - z*d */ 1716 PetscCall(MatMult(jac->H, ilinkA->y, Hu)); /* ||u||_H = u'*H*u */ 1717 PetscCall(VecDot(Hu, ilinkA->y, &nrmz2)); 1718 1719 /* Compute Lower Bound estimate */ 1720 if (iterGKB > jac->gkbdelay) { 1721 lowbnd = 0.0; 1722 for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]); 1723 lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2)); 1724 } 1725 1726 for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2]; 1727 if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd)); 1728 } 1729 1730 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1731 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1732 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1733 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1734 PetscFunctionReturn(PETSC_SUCCESS); 1735 } 1736 1737 #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \ 1738 ((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) || \ 1739 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) || \ 1740 VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE))) 1741 1742 static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y) 1743 { 1744 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1745 PC_FieldSplitLink ilink = jac->head; 1746 PetscInt bs; 1747 1748 PetscFunctionBegin; 1749 if (jac->type == PC_COMPOSITE_ADDITIVE) { 1750 PetscBool matnest; 1751 1752 PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest)); 1753 if (jac->defaultsplit && !matnest) { 1754 PetscCall(VecGetBlockSize(x, &bs)); 1755 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); 1756 PetscCall(VecGetBlockSize(y, &bs)); 1757 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); 1758 PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES)); 1759 while (ilink) { 1760 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1761 PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y)); 1762 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1763 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1764 ilink = ilink->next; 1765 } 1766 PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES)); 1767 } else { 1768 PetscCall(VecSet(y, 0.0)); 1769 while (ilink) { 1770 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1771 ilink = ilink->next; 1772 } 1773 } 1774 } else { 1775 if (!jac->w1) { 1776 PetscCall(VecDuplicate(x, &jac->w1)); 1777 PetscCall(VecDuplicate(x, &jac->w2)); 1778 } 1779 PetscCall(VecSet(y, 0.0)); 1780 if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1781 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1782 while (ilink->next) { 1783 ilink = ilink->next; 1784 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1785 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1786 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1787 } 1788 while (ilink->previous) { 1789 ilink = ilink->previous; 1790 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1791 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1792 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1793 } 1794 } else { 1795 while (ilink->next) { /* get to last entry in linked list */ 1796 ilink = ilink->next; 1797 } 1798 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1799 while (ilink->previous) { 1800 ilink = ilink->previous; 1801 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1802 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1803 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1804 } 1805 } 1806 } 1807 PetscFunctionReturn(PETSC_SUCCESS); 1808 } 1809 1810 static PetscErrorCode PCReset_FieldSplit(PC pc) 1811 { 1812 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1813 PC_FieldSplitLink ilink = jac->head, next; 1814 1815 PetscFunctionBegin; 1816 while (ilink) { 1817 PetscCall(KSPDestroy(&ilink->ksp)); 1818 PetscCall(VecDestroy(&ilink->x)); 1819 PetscCall(VecDestroy(&ilink->y)); 1820 PetscCall(VecDestroy(&ilink->z)); 1821 PetscCall(VecScatterDestroy(&ilink->sctx)); 1822 PetscCall(ISDestroy(&ilink->is)); 1823 PetscCall(ISDestroy(&ilink->is_col)); 1824 PetscCall(PetscFree(ilink->splitname)); 1825 PetscCall(PetscFree(ilink->fields)); 1826 PetscCall(PetscFree(ilink->fields_col)); 1827 next = ilink->next; 1828 PetscCall(PetscFree(ilink)); 1829 ilink = next; 1830 } 1831 jac->head = NULL; 1832 PetscCall(PetscFree2(jac->x, jac->y)); 1833 if (jac->mat && jac->mat != jac->pmat) { 1834 PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat)); 1835 } else if (jac->mat) { 1836 jac->mat = NULL; 1837 } 1838 if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat)); 1839 if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield)); 1840 jac->nsplits = 0; 1841 PetscCall(VecDestroy(&jac->w1)); 1842 PetscCall(VecDestroy(&jac->w2)); 1843 if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL)); 1844 PetscCall(MatDestroy(&jac->schur)); 1845 PetscCall(MatDestroy(&jac->schurp)); 1846 PetscCall(MatDestroy(&jac->schur_user)); 1847 PetscCall(KSPDestroy(&jac->kspschur)); 1848 PetscCall(KSPDestroy(&jac->kspupper)); 1849 PetscCall(MatDestroy(&jac->B)); 1850 PetscCall(MatDestroy(&jac->C)); 1851 PetscCall(MatDestroy(&jac->H)); 1852 PetscCall(VecDestroy(&jac->u)); 1853 PetscCall(VecDestroy(&jac->v)); 1854 PetscCall(VecDestroy(&jac->Hu)); 1855 PetscCall(VecDestroy(&jac->d)); 1856 PetscCall(PetscFree(jac->vecz)); 1857 PetscCall(PetscViewerDestroy(&jac->gkbviewer)); 1858 jac->isrestrict = PETSC_FALSE; 1859 PetscFunctionReturn(PETSC_SUCCESS); 1860 } 1861 1862 static PetscErrorCode PCDestroy_FieldSplit(PC pc) 1863 { 1864 PetscFunctionBegin; 1865 PetscCall(PCReset_FieldSplit(pc)); 1866 PetscCall(PetscFree(pc->data)); 1867 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL)); 1868 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL)); 1869 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL)); 1870 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL)); 1871 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL)); 1872 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL)); 1873 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL)); 1874 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL)); 1875 1876 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL)); 1877 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL)); 1878 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL)); 1879 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL)); 1880 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL)); 1881 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL)); 1882 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL)); 1883 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL)); 1884 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL)); 1885 PetscFunctionReturn(PETSC_SUCCESS); 1886 } 1887 1888 static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject) 1889 { 1890 PetscInt bs; 1891 PetscBool flg; 1892 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1893 PCCompositeType ctype; 1894 1895 PetscFunctionBegin; 1896 PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options"); 1897 PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL)); 1898 PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg)); 1899 if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs)); 1900 jac->diag_use_amat = pc->useAmat; 1901 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)); 1902 jac->offdiag_use_amat = pc->useAmat; 1903 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)); 1904 PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL)); 1905 PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */ 1906 PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg)); 1907 if (flg) PetscCall(PCFieldSplitSetType(pc, ctype)); 1908 /* Only setup fields once */ 1909 if ((jac->bs > 0) && (jac->nsplits == 0)) { 1910 /* only allow user to set fields from command line. 1911 otherwise user can set them in PCFieldSplitSetDefaults() */ 1912 PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc)); 1913 if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n")); 1914 } 1915 if (jac->type == PC_COMPOSITE_SCHUR) { 1916 PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg)); 1917 if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n")); 1918 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)); 1919 PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL)); 1920 PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL)); 1921 } else if (jac->type == PC_COMPOSITE_GKB) { 1922 PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL)); 1923 PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL)); 1924 PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0)); 1925 PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL)); 1926 PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL)); 1927 } 1928 /* 1929 In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet. 1930 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 1931 is called on the outer solver in case changes were made in the options database 1932 1933 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() 1934 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. 1935 Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types. 1936 1937 There could be a negative side effect of calling the KSPSetFromOptions() below. 1938 1939 If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call 1940 */ 1941 if (jac->issetup) { 1942 PC_FieldSplitLink ilink = jac->head; 1943 if (jac->type == PC_COMPOSITE_SCHUR) { 1944 if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper)); 1945 if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur)); 1946 } 1947 while (ilink) { 1948 if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp)); 1949 ilink = ilink->next; 1950 } 1951 } 1952 PetscOptionsHeadEnd(); 1953 PetscFunctionReturn(PETSC_SUCCESS); 1954 } 1955 1956 static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col) 1957 { 1958 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1959 PC_FieldSplitLink ilink, next = jac->head; 1960 char prefix[128]; 1961 PetscInt i; 1962 1963 PetscFunctionBegin; 1964 if (jac->splitdefined) { 1965 PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname)); 1966 PetscFunctionReturn(PETSC_SUCCESS); 1967 } 1968 for (i = 0; i < n; i++) { PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]); } 1969 PetscCall(PetscNew(&ilink)); 1970 if (splitname) { 1971 PetscCall(PetscStrallocpy(splitname, &ilink->splitname)); 1972 } else { 1973 PetscCall(PetscMalloc1(3, &ilink->splitname)); 1974 PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits)); 1975 } 1976 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 */ 1977 PetscCall(PetscMalloc1(n, &ilink->fields)); 1978 PetscCall(PetscArraycpy(ilink->fields, fields, n)); 1979 PetscCall(PetscMalloc1(n, &ilink->fields_col)); 1980 PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n)); 1981 1982 ilink->nfields = n; 1983 ilink->next = NULL; 1984 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp)); 1985 PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel)); 1986 PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure)); 1987 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1)); 1988 PetscCall(KSPSetType(ilink->ksp, KSPPREONLY)); 1989 1990 PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 1991 PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix)); 1992 1993 if (!next) { 1994 jac->head = ilink; 1995 ilink->previous = NULL; 1996 } else { 1997 while (next->next) next = next->next; 1998 next->next = ilink; 1999 ilink->previous = next; 2000 } 2001 jac->nsplits++; 2002 PetscFunctionReturn(PETSC_SUCCESS); 2003 } 2004 2005 static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp) 2006 { 2007 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2008 2009 PetscFunctionBegin; 2010 *subksp = NULL; 2011 if (n) *n = 0; 2012 if (jac->type == PC_COMPOSITE_SCHUR) { 2013 PetscInt nn; 2014 2015 PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()"); 2016 PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits); 2017 nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0); 2018 PetscCall(PetscMalloc1(nn, subksp)); 2019 (*subksp)[0] = jac->head->ksp; 2020 (*subksp)[1] = jac->kspschur; 2021 if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper; 2022 if (n) *n = nn; 2023 } 2024 PetscFunctionReturn(PETSC_SUCCESS); 2025 } 2026 2027 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp) 2028 { 2029 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2030 2031 PetscFunctionBegin; 2032 PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()"); 2033 PetscCall(PetscMalloc1(jac->nsplits, subksp)); 2034 PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp)); 2035 2036 (*subksp)[1] = jac->kspschur; 2037 if (n) *n = jac->nsplits; 2038 PetscFunctionReturn(PETSC_SUCCESS); 2039 } 2040 2041 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp) 2042 { 2043 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2044 PetscInt cnt = 0; 2045 PC_FieldSplitLink ilink = jac->head; 2046 2047 PetscFunctionBegin; 2048 PetscCall(PetscMalloc1(jac->nsplits, subksp)); 2049 while (ilink) { 2050 (*subksp)[cnt++] = ilink->ksp; 2051 ilink = ilink->next; 2052 } 2053 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); 2054 if (n) *n = jac->nsplits; 2055 PetscFunctionReturn(PETSC_SUCCESS); 2056 } 2057 2058 /*@ 2059 PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`. 2060 2061 Input Parameters: 2062 + pc - the preconditioner context 2063 - isy - the index set that defines the indices to which the fieldsplit is to be restricted 2064 2065 Level: advanced 2066 2067 Developer Notes: 2068 It seems the resulting `IS`s will not cover the entire space, so 2069 how can they define a convergent preconditioner? Needs explaining. 2070 2071 .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 2072 @*/ 2073 PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy) 2074 { 2075 PetscFunctionBegin; 2076 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2077 PetscValidHeaderSpecific(isy, IS_CLASSID, 2); 2078 PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy)); 2079 PetscFunctionReturn(PETSC_SUCCESS); 2080 } 2081 2082 static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy) 2083 { 2084 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2085 PC_FieldSplitLink ilink = jac->head, next; 2086 PetscInt localsize, size, sizez, i; 2087 const PetscInt *ind, *indz; 2088 PetscInt *indc, *indcz; 2089 PetscBool flg; 2090 2091 PetscFunctionBegin; 2092 PetscCall(ISGetLocalSize(isy, &localsize)); 2093 PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy))); 2094 size -= localsize; 2095 while (ilink) { 2096 IS isrl, isr; 2097 PC subpc; 2098 PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl)); 2099 PetscCall(ISGetLocalSize(isrl, &localsize)); 2100 PetscCall(PetscMalloc1(localsize, &indc)); 2101 PetscCall(ISGetIndices(isrl, &ind)); 2102 PetscCall(PetscArraycpy(indc, ind, localsize)); 2103 PetscCall(ISRestoreIndices(isrl, &ind)); 2104 PetscCall(ISDestroy(&isrl)); 2105 for (i = 0; i < localsize; i++) *(indc + i) += size; 2106 PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr)); 2107 PetscCall(PetscObjectReference((PetscObject)isr)); 2108 PetscCall(ISDestroy(&ilink->is)); 2109 ilink->is = isr; 2110 PetscCall(PetscObjectReference((PetscObject)isr)); 2111 PetscCall(ISDestroy(&ilink->is_col)); 2112 ilink->is_col = isr; 2113 PetscCall(ISDestroy(&isr)); 2114 PetscCall(KSPGetPC(ilink->ksp, &subpc)); 2115 PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg)); 2116 if (flg) { 2117 IS iszl, isz; 2118 MPI_Comm comm; 2119 PetscCall(ISGetLocalSize(ilink->is, &localsize)); 2120 comm = PetscObjectComm((PetscObject)ilink->is); 2121 PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl)); 2122 PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm)); 2123 sizez -= localsize; 2124 PetscCall(ISGetLocalSize(iszl, &localsize)); 2125 PetscCall(PetscMalloc1(localsize, &indcz)); 2126 PetscCall(ISGetIndices(iszl, &indz)); 2127 PetscCall(PetscArraycpy(indcz, indz, localsize)); 2128 PetscCall(ISRestoreIndices(iszl, &indz)); 2129 PetscCall(ISDestroy(&iszl)); 2130 for (i = 0; i < localsize; i++) *(indcz + i) += sizez; 2131 PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz)); 2132 PetscCall(PCFieldSplitRestrictIS(subpc, isz)); 2133 PetscCall(ISDestroy(&isz)); 2134 } 2135 next = ilink->next; 2136 ilink = next; 2137 } 2138 jac->isrestrict = PETSC_TRUE; 2139 PetscFunctionReturn(PETSC_SUCCESS); 2140 } 2141 2142 static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is) 2143 { 2144 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2145 PC_FieldSplitLink ilink, next = jac->head; 2146 char prefix[128]; 2147 2148 PetscFunctionBegin; 2149 if (jac->splitdefined) { 2150 PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname)); 2151 PetscFunctionReturn(PETSC_SUCCESS); 2152 } 2153 PetscCall(PetscNew(&ilink)); 2154 if (splitname) { 2155 PetscCall(PetscStrallocpy(splitname, &ilink->splitname)); 2156 } else { 2157 PetscCall(PetscMalloc1(8, &ilink->splitname)); 2158 PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits)); 2159 } 2160 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 */ 2161 PetscCall(PetscObjectReference((PetscObject)is)); 2162 PetscCall(ISDestroy(&ilink->is)); 2163 ilink->is = is; 2164 PetscCall(PetscObjectReference((PetscObject)is)); 2165 PetscCall(ISDestroy(&ilink->is_col)); 2166 ilink->is_col = is; 2167 ilink->next = NULL; 2168 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp)); 2169 PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel)); 2170 PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure)); 2171 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1)); 2172 PetscCall(KSPSetType(ilink->ksp, KSPPREONLY)); 2173 2174 PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 2175 PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix)); 2176 2177 if (!next) { 2178 jac->head = ilink; 2179 ilink->previous = NULL; 2180 } else { 2181 while (next->next) next = next->next; 2182 next->next = ilink; 2183 ilink->previous = next; 2184 } 2185 jac->nsplits++; 2186 PetscFunctionReturn(PETSC_SUCCESS); 2187 } 2188 2189 /*@ 2190 PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT` 2191 2192 Logically Collective 2193 2194 Input Parameters: 2195 + pc - the preconditioner context 2196 . splitname - name of this split, if `NULL` the number of the split is used 2197 . n - the number of fields in this split 2198 . fields - the fields in this split 2199 - fields_col - generally the same as `fields`, if it does not match `fields` then the submatrix that is solved for this set of fields comes from an off-diagonal block 2200 of the matrix and `fields_col` provides the column indices for that block 2201 2202 Options Database Key: 2203 . -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split 2204 2205 Level: intermediate 2206 2207 Notes: 2208 Use `PCFieldSplitSetIS()` to set a general set of indices as a split. 2209 2210 If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`. 2211 2212 If the matrix used to construct the preconditioner is not `MATNEST` then 2213 `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlocksize()` or 2214 to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block 2215 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 2216 0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x.... 2217 where the numbered entries indicate what is in the split. 2218 2219 This function is called once per split (it creates a new split each time). Solve options 2220 for this split will be available under the prefix `-fieldsplit_SPLITNAME_`. 2221 2222 `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields` 2223 2224 Developer Notes: 2225 This routine does not actually create the `IS` representing the split, that is delayed 2226 until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be 2227 available when this routine is called. 2228 2229 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`, 2230 `MatSetBlocksize()`, `MatCreateNest()` 2231 @*/ 2232 PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[]) 2233 { 2234 PetscFunctionBegin; 2235 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2236 PetscAssertPointer(splitname, 2); 2237 PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname); 2238 PetscAssertPointer(fields, 4); 2239 PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col)); 2240 PetscFunctionReturn(PETSC_SUCCESS); 2241 } 2242 2243 /*@ 2244 PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build 2245 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2246 2247 Logically Collective 2248 2249 Input Parameters: 2250 + pc - the preconditioner object 2251 - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from 2252 2253 Options Database Key: 2254 . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks 2255 2256 Level: intermediate 2257 2258 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT` 2259 @*/ 2260 PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg) 2261 { 2262 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2263 PetscBool isfs; 2264 2265 PetscFunctionBegin; 2266 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2267 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2268 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2269 jac->diag_use_amat = flg; 2270 PetscFunctionReturn(PETSC_SUCCESS); 2271 } 2272 2273 /*@ 2274 PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build 2275 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2276 2277 Logically Collective 2278 2279 Input Parameter: 2280 . pc - the preconditioner object 2281 2282 Output Parameter: 2283 . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from 2284 2285 Level: intermediate 2286 2287 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT` 2288 @*/ 2289 PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg) 2290 { 2291 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2292 PetscBool isfs; 2293 2294 PetscFunctionBegin; 2295 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2296 PetscAssertPointer(flg, 2); 2297 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2298 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2299 *flg = jac->diag_use_amat; 2300 PetscFunctionReturn(PETSC_SUCCESS); 2301 } 2302 2303 /*@ 2304 PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build 2305 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2306 2307 Logically Collective 2308 2309 Input Parameters: 2310 + pc - the preconditioner object 2311 - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from 2312 2313 Options Database Key: 2314 . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks 2315 2316 Level: intermediate 2317 2318 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT` 2319 @*/ 2320 PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg) 2321 { 2322 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2323 PetscBool isfs; 2324 2325 PetscFunctionBegin; 2326 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2327 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2328 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2329 jac->offdiag_use_amat = flg; 2330 PetscFunctionReturn(PETSC_SUCCESS); 2331 } 2332 2333 /*@ 2334 PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build 2335 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2336 2337 Logically Collective 2338 2339 Input Parameter: 2340 . pc - the preconditioner object 2341 2342 Output Parameter: 2343 . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from 2344 2345 Level: intermediate 2346 2347 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT` 2348 @*/ 2349 PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg) 2350 { 2351 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2352 PetscBool isfs; 2353 2354 PetscFunctionBegin; 2355 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2356 PetscAssertPointer(flg, 2); 2357 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2358 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2359 *flg = jac->offdiag_use_amat; 2360 PetscFunctionReturn(PETSC_SUCCESS); 2361 } 2362 2363 /*@ 2364 PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT` 2365 2366 Logically Collective 2367 2368 Input Parameters: 2369 + pc - the preconditioner context 2370 . splitname - name of this split, if `NULL` the number of the split is used 2371 - is - the index set that defines the elements in this split 2372 2373 Level: intermediate 2374 2375 Notes: 2376 Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST` 2377 2378 This function is called once per split (it creates a new split each time). Solve options 2379 for this split will be available under the prefix -fieldsplit_SPLITNAME_. 2380 2381 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()` 2382 @*/ 2383 PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is) 2384 { 2385 PetscFunctionBegin; 2386 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2387 if (splitname) PetscAssertPointer(splitname, 2); 2388 PetscValidHeaderSpecific(is, IS_CLASSID, 3); 2389 PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is)); 2390 PetscFunctionReturn(PETSC_SUCCESS); 2391 } 2392 2393 /*@ 2394 PCFieldSplitGetIS - Retrieves the elements for a split as an `IS` 2395 2396 Logically Collective 2397 2398 Input Parameters: 2399 + pc - the preconditioner context 2400 - splitname - name of this split 2401 2402 Output Parameter: 2403 . is - the index set that defines the elements in this split, or `NULL` if the split is not found 2404 2405 Level: intermediate 2406 2407 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()` 2408 @*/ 2409 PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is) 2410 { 2411 PetscFunctionBegin; 2412 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2413 PetscAssertPointer(splitname, 2); 2414 PetscAssertPointer(is, 3); 2415 { 2416 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2417 PC_FieldSplitLink ilink = jac->head; 2418 PetscBool found; 2419 2420 *is = NULL; 2421 while (ilink) { 2422 PetscCall(PetscStrcmp(ilink->splitname, splitname, &found)); 2423 if (found) { 2424 *is = ilink->is; 2425 break; 2426 } 2427 ilink = ilink->next; 2428 } 2429 } 2430 PetscFunctionReturn(PETSC_SUCCESS); 2431 } 2432 2433 /*@ 2434 PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS` 2435 2436 Logically Collective 2437 2438 Input Parameters: 2439 + pc - the preconditioner context 2440 - index - index of this split 2441 2442 Output Parameter: 2443 . is - the index set that defines the elements in this split 2444 2445 Level: intermediate 2446 2447 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`, 2448 2449 @*/ 2450 PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is) 2451 { 2452 PetscFunctionBegin; 2453 PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index); 2454 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2455 PetscAssertPointer(is, 3); 2456 { 2457 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2458 PC_FieldSplitLink ilink = jac->head; 2459 PetscInt i = 0; 2460 PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits); 2461 2462 while (i < index) { 2463 ilink = ilink->next; 2464 ++i; 2465 } 2466 PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is)); 2467 } 2468 PetscFunctionReturn(PETSC_SUCCESS); 2469 } 2470 2471 /*@ 2472 PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the 2473 fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used. 2474 2475 Logically Collective 2476 2477 Input Parameters: 2478 + pc - the preconditioner context 2479 - bs - the block size 2480 2481 Level: intermediate 2482 2483 Note: 2484 If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields. 2485 2486 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 2487 @*/ 2488 PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs) 2489 { 2490 PetscFunctionBegin; 2491 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2492 PetscValidLogicalCollectiveInt(pc, bs, 2); 2493 PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs)); 2494 PetscFunctionReturn(PETSC_SUCCESS); 2495 } 2496 2497 /*@C 2498 PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits 2499 2500 Collective 2501 2502 Input Parameter: 2503 . pc - the preconditioner context 2504 2505 Output Parameters: 2506 + n - the number of splits 2507 - subksp - the array of `KSP` contexts 2508 2509 Level: advanced 2510 2511 Notes: 2512 After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()` 2513 (not the `KSP`, just the array that contains them). 2514 2515 You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`. 2516 2517 If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the 2518 Schur complement and the `KSP` object used to iterate over the Schur complement. 2519 To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`. 2520 2521 If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the 2522 inner linear system defined by the matrix H in each loop. 2523 2524 Fortran Notes: 2525 You must pass in a `KSP` array that is large enough to contain all the `KSP`s. 2526 You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the 2527 `KSP` array must be. 2528 2529 Developer Notes: 2530 There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()` 2531 2532 The Fortran interface could be modernized to return directly the array of values. 2533 2534 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()` 2535 @*/ 2536 PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[]) 2537 { 2538 PetscFunctionBegin; 2539 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2540 if (n) PetscAssertPointer(n, 2); 2541 PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp)); 2542 PetscFunctionReturn(PETSC_SUCCESS); 2543 } 2544 2545 /*@C 2546 PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT` 2547 2548 Collective 2549 2550 Input Parameter: 2551 . pc - the preconditioner context 2552 2553 Output Parameters: 2554 + n - the number of splits 2555 - subksp - the array of `KSP` contexts 2556 2557 Level: advanced 2558 2559 Notes: 2560 After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()` 2561 (not the `KSP` just the array that contains them). 2562 2563 You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`. 2564 2565 If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order) 2566 + 1 - the `KSP` used for the (1,1) block 2567 . 2 - the `KSP` used for the Schur complement (not the one used for the interior Schur solver) 2568 - 3 - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block). 2569 2570 It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`. 2571 2572 Fortran Notes: 2573 You must pass in a `KSP` array that is large enough to contain all the local `KSP`s. 2574 You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the 2575 `KSP` array must be. 2576 2577 Developer Notes: 2578 There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()` 2579 2580 Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged? 2581 2582 The Fortran interface should be modernized to return directly the array of values. 2583 2584 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()` 2585 @*/ 2586 PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[]) 2587 { 2588 PetscFunctionBegin; 2589 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2590 if (n) PetscAssertPointer(n, 2); 2591 PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp)); 2592 PetscFunctionReturn(PETSC_SUCCESS); 2593 } 2594 2595 /*@ 2596 PCFieldSplitSetSchurPre - Indicates from what operator the preconditioner is constructed for the Schur complement. 2597 The default is the A11 matrix. 2598 2599 Collective 2600 2601 Input Parameters: 2602 + pc - the preconditioner context 2603 . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default), 2604 `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`, 2605 `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL` 2606 - pre - matrix to use for preconditioning, or `NULL` 2607 2608 Options Database Keys: 2609 + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments 2610 - -fieldsplit_1_pc_type <pctype> - the preconditioner algorithm that is used to construct the preconditioner from the operator 2611 2612 Level: intermediate 2613 2614 Notes: 2615 If ptype is 2616 + a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner 2617 matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix 2618 . self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix: 2619 The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM` 2620 . user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument 2621 to this function). 2622 . selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $ 2623 This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be 2624 lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump` 2625 - full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation 2626 computed internally by `PCFIELDSPLIT` (this is expensive) 2627 useful mostly as a test that the Schur complement approach can work for your problem 2628 2629 When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense 2630 with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and 2631 `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement. 2632 2633 Developer Note: 2634 The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere. 2635 2636 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, 2637 `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()` 2638 @*/ 2639 PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2640 { 2641 PetscFunctionBegin; 2642 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2643 PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre)); 2644 PetscFunctionReturn(PETSC_SUCCESS); 2645 } 2646 2647 PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2648 { 2649 return PCFieldSplitSetSchurPre(pc, ptype, pre); 2650 } /* Deprecated name */ 2651 2652 /*@ 2653 PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be 2654 preconditioned. See `PCFieldSplitSetSchurPre()` for details. 2655 2656 Logically Collective 2657 2658 Input Parameter: 2659 . pc - the preconditioner context 2660 2661 Output Parameters: 2662 + 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` 2663 - pre - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL` 2664 2665 Level: intermediate 2666 2667 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC` 2668 @*/ 2669 PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre) 2670 { 2671 PetscFunctionBegin; 2672 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2673 PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre)); 2674 PetscFunctionReturn(PETSC_SUCCESS); 2675 } 2676 2677 /*@ 2678 PCFieldSplitSchurGetS - extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately 2679 2680 Not Collective 2681 2682 Input Parameter: 2683 . pc - the preconditioner context 2684 2685 Output Parameter: 2686 . S - the Schur complement matrix 2687 2688 Level: advanced 2689 2690 Note: 2691 This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`. 2692 2693 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`, 2694 `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()` 2695 @*/ 2696 PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S) 2697 { 2698 const char *t; 2699 PetscBool isfs; 2700 PC_FieldSplit *jac; 2701 2702 PetscFunctionBegin; 2703 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2704 PetscCall(PetscObjectGetType((PetscObject)pc, &t)); 2705 PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs)); 2706 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t); 2707 jac = (PC_FieldSplit *)pc->data; 2708 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type); 2709 if (S) *S = jac->schur; 2710 PetscFunctionReturn(PETSC_SUCCESS); 2711 } 2712 2713 /*@ 2714 PCFieldSplitSchurRestoreS - returns the `MATSCHURCOMPLEMENT` matrix used by this `PC` 2715 2716 Not Collective 2717 2718 Input Parameters: 2719 + pc - the preconditioner context 2720 - S - the Schur complement matrix 2721 2722 Level: advanced 2723 2724 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()` 2725 @*/ 2726 PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S) 2727 { 2728 const char *t; 2729 PetscBool isfs; 2730 PC_FieldSplit *jac; 2731 2732 PetscFunctionBegin; 2733 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2734 PetscCall(PetscObjectGetType((PetscObject)pc, &t)); 2735 PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs)); 2736 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t); 2737 jac = (PC_FieldSplit *)pc->data; 2738 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type); 2739 PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten"); 2740 PetscFunctionReturn(PETSC_SUCCESS); 2741 } 2742 2743 static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2744 { 2745 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2746 2747 PetscFunctionBegin; 2748 jac->schurpre = ptype; 2749 if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) { 2750 PetscCall(MatDestroy(&jac->schur_user)); 2751 jac->schur_user = pre; 2752 PetscCall(PetscObjectReference((PetscObject)jac->schur_user)); 2753 } 2754 PetscFunctionReturn(PETSC_SUCCESS); 2755 } 2756 2757 static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre) 2758 { 2759 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2760 2761 PetscFunctionBegin; 2762 if (ptype) *ptype = jac->schurpre; 2763 if (pre) *pre = jac->schur_user; 2764 PetscFunctionReturn(PETSC_SUCCESS); 2765 } 2766 2767 /*@ 2768 PCFieldSplitSetSchurFactType - sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note` 2769 2770 Collective 2771 2772 Input Parameters: 2773 + pc - the preconditioner context 2774 - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default 2775 2776 Options Database Key: 2777 . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full` 2778 2779 Level: intermediate 2780 2781 Notes: 2782 The FULL factorization is 2783 2784 ```{math} 2785 \left(\begin{array}{cc} A & B \\ 2786 C & E \\ 2787 \end{array}\right) = 2788 \left(\begin{array}{cc} 1 & 0 \\ 2789 C*A^{-1} & I \\ 2790 \end{array}\right) 2791 \left(\begin{array}{cc} A & 0 \\ 2792 0 & S \\ 2793 \end{array}\right) 2794 \left(\begin{array}{cc} I & A^{-1}B \\ 2795 0 & I \\ 2796 \end{array}\right) = L D U. 2797 ``` 2798 2799 where $ S = E - C*A^{-1}*B $. In practice, the full factorization is applied via block triangular solves with the grouping $L*(D*U)$. UPPER uses $D*U$, LOWER uses $L*D$, 2800 and DIAG is the diagonal part with the sign of $ S $ flipped (because this makes the preconditioner positive definite for many formulations, 2801 thus allowing the use of `KSPMINRES)`. Sign flipping of $ S $ can be turned off with `PCFieldSplitSetSchurScale()`. 2802 2803 If $A$ and $S$ are solved exactly 2804 + 1 - FULL factorization is a direct solver. 2805 . 2 - 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. 2806 - 3 - 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. 2807 2808 If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner 2809 application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice. 2810 2811 For symmetric problems in which $A$ is positive definite and $S$ is negative definite, DIAG can be used with `KSPMINRES`. 2812 2813 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). 2814 2815 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`, 2816 [](sec_flexibleksp), `PCFieldSplitSetSchurPre()` 2817 @*/ 2818 PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype) 2819 { 2820 PetscFunctionBegin; 2821 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2822 PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype)); 2823 PetscFunctionReturn(PETSC_SUCCESS); 2824 } 2825 2826 static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype) 2827 { 2828 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2829 2830 PetscFunctionBegin; 2831 jac->schurfactorization = ftype; 2832 PetscFunctionReturn(PETSC_SUCCESS); 2833 } 2834 2835 /*@ 2836 PCFieldSplitSetSchurScale - Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`. 2837 2838 Collective 2839 2840 Input Parameters: 2841 + pc - the preconditioner context 2842 - scale - scaling factor for the Schur complement 2843 2844 Options Database Key: 2845 . -pc_fieldsplit_schur_scale <scale> - default is -1.0 2846 2847 Level: intermediate 2848 2849 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()` 2850 @*/ 2851 PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale) 2852 { 2853 PetscFunctionBegin; 2854 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2855 PetscValidLogicalCollectiveScalar(pc, scale, 2); 2856 PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale)); 2857 PetscFunctionReturn(PETSC_SUCCESS); 2858 } 2859 2860 static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale) 2861 { 2862 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2863 2864 PetscFunctionBegin; 2865 jac->schurscale = scale; 2866 PetscFunctionReturn(PETSC_SUCCESS); 2867 } 2868 2869 /*@C 2870 PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement 2871 2872 Collective 2873 2874 Input Parameter: 2875 . pc - the preconditioner context 2876 2877 Output Parameters: 2878 + A00 - the (0,0) block 2879 . A01 - the (0,1) block 2880 . A10 - the (1,0) block 2881 - A11 - the (1,1) block 2882 2883 Level: advanced 2884 2885 Note: 2886 Use `NULL` for any unneeded output arguments 2887 2888 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()` 2889 @*/ 2890 PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11) 2891 { 2892 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2893 2894 PetscFunctionBegin; 2895 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2896 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach."); 2897 if (A00) *A00 = jac->pmat[0]; 2898 if (A01) *A01 = jac->B; 2899 if (A10) *A10 = jac->C; 2900 if (A11) *A11 = jac->pmat[1]; 2901 PetscFunctionReturn(PETSC_SUCCESS); 2902 } 2903 2904 /*@ 2905 PCFieldSplitSetGKBTol - Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 2906 2907 Collective 2908 2909 Input Parameters: 2910 + pc - the preconditioner context 2911 - tolerance - the solver tolerance 2912 2913 Options Database Key: 2914 . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5 2915 2916 Level: intermediate 2917 2918 Note: 2919 The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion. 2920 It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than 2921 this estimate, the stopping criterion is satisfactory in practical cases. 2922 2923 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()` 2924 @*/ 2925 PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance) 2926 { 2927 PetscFunctionBegin; 2928 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2929 PetscValidLogicalCollectiveReal(pc, tolerance, 2); 2930 PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance)); 2931 PetscFunctionReturn(PETSC_SUCCESS); 2932 } 2933 2934 static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance) 2935 { 2936 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2937 2938 PetscFunctionBegin; 2939 jac->gkbtol = tolerance; 2940 PetscFunctionReturn(PETSC_SUCCESS); 2941 } 2942 2943 /*@ 2944 PCFieldSplitSetGKBMaxit - Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 2945 2946 Collective 2947 2948 Input Parameters: 2949 + pc - the preconditioner context 2950 - maxit - the maximum number of iterations 2951 2952 Options Database Key: 2953 . -pc_fieldsplit_gkb_maxit <maxit> - default is 100 2954 2955 Level: intermediate 2956 2957 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()` 2958 @*/ 2959 PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit) 2960 { 2961 PetscFunctionBegin; 2962 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2963 PetscValidLogicalCollectiveInt(pc, maxit, 2); 2964 PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit)); 2965 PetscFunctionReturn(PETSC_SUCCESS); 2966 } 2967 2968 static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit) 2969 { 2970 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2971 2972 PetscFunctionBegin; 2973 jac->gkbmaxit = maxit; 2974 PetscFunctionReturn(PETSC_SUCCESS); 2975 } 2976 2977 /*@ 2978 PCFieldSplitSetGKBDelay - Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT` 2979 preconditioner. 2980 2981 Collective 2982 2983 Input Parameters: 2984 + pc - the preconditioner context 2985 - delay - the delay window in the lower bound estimate 2986 2987 Options Database Key: 2988 . -pc_fieldsplit_gkb_delay <delay> - default is 5 2989 2990 Level: intermediate 2991 2992 Notes: 2993 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 $ 2994 is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs 2995 at least (`delay` + 1) iterations to stop. 2996 2997 For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013` 2998 2999 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()` 3000 @*/ 3001 PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay) 3002 { 3003 PetscFunctionBegin; 3004 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3005 PetscValidLogicalCollectiveInt(pc, delay, 2); 3006 PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay)); 3007 PetscFunctionReturn(PETSC_SUCCESS); 3008 } 3009 3010 static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay) 3011 { 3012 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3013 3014 PetscFunctionBegin; 3015 jac->gkbdelay = delay; 3016 PetscFunctionReturn(PETSC_SUCCESS); 3017 } 3018 3019 /*@ 3020 PCFieldSplitSetGKBNu - Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the 3021 Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 3022 3023 Collective 3024 3025 Input Parameters: 3026 + pc - the preconditioner context 3027 - nu - the shift parameter 3028 3029 Options Database Key: 3030 . -pc_fieldsplit_gkb_nu <nu> - default is 1 3031 3032 Level: intermediate 3033 3034 Notes: 3035 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, 3036 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 3037 necessary to find a good balance in between the convergence of the inner and outer loop. 3038 3039 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. 3040 3041 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()` 3042 @*/ 3043 PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu) 3044 { 3045 PetscFunctionBegin; 3046 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3047 PetscValidLogicalCollectiveReal(pc, nu, 2); 3048 PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu)); 3049 PetscFunctionReturn(PETSC_SUCCESS); 3050 } 3051 3052 static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu) 3053 { 3054 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3055 3056 PetscFunctionBegin; 3057 jac->gkbnu = nu; 3058 PetscFunctionReturn(PETSC_SUCCESS); 3059 } 3060 3061 static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type) 3062 { 3063 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3064 3065 PetscFunctionBegin; 3066 jac->type = type; 3067 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL)); 3068 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL)); 3069 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL)); 3070 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL)); 3071 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL)); 3072 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL)); 3073 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL)); 3074 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL)); 3075 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL)); 3076 3077 if (type == PC_COMPOSITE_SCHUR) { 3078 pc->ops->apply = PCApply_FieldSplit_Schur; 3079 pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur; 3080 pc->ops->view = PCView_FieldSplit_Schur; 3081 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit_Schur; 3082 3083 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur)); 3084 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit)); 3085 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit)); 3086 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit)); 3087 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit)); 3088 } else if (type == PC_COMPOSITE_GKB) { 3089 pc->ops->apply = PCApply_FieldSplit_GKB; 3090 pc->ops->view = PCView_FieldSplit_GKB; 3091 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit_GKB; 3092 3093 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit)); 3094 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit)); 3095 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit)); 3096 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit)); 3097 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit)); 3098 } else { 3099 pc->ops->apply = PCApply_FieldSplit; 3100 pc->ops->view = PCView_FieldSplit; 3101 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit; 3102 3103 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit)); 3104 } 3105 PetscFunctionReturn(PETSC_SUCCESS); 3106 } 3107 3108 static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs) 3109 { 3110 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3111 3112 PetscFunctionBegin; 3113 PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs); 3114 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); 3115 jac->bs = bs; 3116 PetscFunctionReturn(PETSC_SUCCESS); 3117 } 3118 3119 static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[]) 3120 { 3121 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3122 PC_FieldSplitLink ilink_current = jac->head; 3123 IS is_owned; 3124 3125 PetscFunctionBegin; 3126 jac->coordinates_set = PETSC_TRUE; // Internal flag 3127 PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL)); 3128 3129 while (ilink_current) { 3130 // For each IS, embed it to get local coords indces 3131 IS is_coords; 3132 PetscInt ndofs_block; 3133 const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block 3134 3135 // Setting drop to true for safety. It should make no difference. 3136 PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords)); 3137 PetscCall(ISGetLocalSize(is_coords, &ndofs_block)); 3138 PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration)); 3139 3140 // Allocate coordinates vector and set it directly 3141 PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords)); 3142 for (PetscInt dof = 0; dof < ndofs_block; ++dof) { 3143 for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d]; 3144 } 3145 ilink_current->dim = dim; 3146 ilink_current->ndofs = ndofs_block; 3147 PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration)); 3148 PetscCall(ISDestroy(&is_coords)); 3149 ilink_current = ilink_current->next; 3150 } 3151 PetscCall(ISDestroy(&is_owned)); 3152 PetscFunctionReturn(PETSC_SUCCESS); 3153 } 3154 3155 /*@ 3156 PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT` 3157 3158 Collective 3159 3160 Input Parameters: 3161 + pc - the preconditioner context 3162 - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, 3163 `PC_COMPOSITE_GKB` 3164 3165 Options Database Key: 3166 . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type 3167 3168 Level: intermediate 3169 3170 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, 3171 `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()` 3172 @*/ 3173 PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type) 3174 { 3175 PetscFunctionBegin; 3176 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3177 PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type)); 3178 PetscFunctionReturn(PETSC_SUCCESS); 3179 } 3180 3181 /*@ 3182 PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT` 3183 3184 Not collective 3185 3186 Input Parameter: 3187 . pc - the preconditioner context 3188 3189 Output Parameter: 3190 . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR` 3191 3192 Level: intermediate 3193 3194 .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, 3195 `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR` 3196 @*/ 3197 PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type) 3198 { 3199 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3200 3201 PetscFunctionBegin; 3202 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3203 PetscAssertPointer(type, 2); 3204 *type = jac->type; 3205 PetscFunctionReturn(PETSC_SUCCESS); 3206 } 3207 3208 /*@ 3209 PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible. 3210 3211 Logically Collective 3212 3213 Input Parameters: 3214 + pc - the preconditioner context 3215 - flg - boolean indicating whether to use field splits defined by the `DM` 3216 3217 Options Database Key: 3218 . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM` 3219 3220 Level: intermediate 3221 3222 Developer Note: 3223 The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database 3224 3225 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()` 3226 @*/ 3227 PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg) 3228 { 3229 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3230 PetscBool isfs; 3231 3232 PetscFunctionBegin; 3233 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3234 PetscValidLogicalCollectiveBool(pc, flg, 2); 3235 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 3236 if (isfs) jac->dm_splits = flg; 3237 PetscFunctionReturn(PETSC_SUCCESS); 3238 } 3239 3240 /*@ 3241 PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible. 3242 3243 Logically Collective 3244 3245 Input Parameter: 3246 . pc - the preconditioner context 3247 3248 Output Parameter: 3249 . flg - boolean indicating whether to use field splits defined by the `DM` 3250 3251 Level: intermediate 3252 3253 Developer Note: 3254 The name should be `PCFieldSplitGetUseDMSplits()` 3255 3256 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()` 3257 @*/ 3258 PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg) 3259 { 3260 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3261 PetscBool isfs; 3262 3263 PetscFunctionBegin; 3264 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3265 PetscAssertPointer(flg, 2); 3266 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 3267 if (isfs) { 3268 if (flg) *flg = jac->dm_splits; 3269 } 3270 PetscFunctionReturn(PETSC_SUCCESS); 3271 } 3272 3273 /*@ 3274 PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries. 3275 3276 Logically Collective 3277 3278 Input Parameter: 3279 . pc - the preconditioner context 3280 3281 Output Parameter: 3282 . flg - boolean indicating whether to detect fields or not 3283 3284 Level: intermediate 3285 3286 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()` 3287 @*/ 3288 PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg) 3289 { 3290 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3291 3292 PetscFunctionBegin; 3293 *flg = jac->detect; 3294 PetscFunctionReturn(PETSC_SUCCESS); 3295 } 3296 3297 /*@ 3298 PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries. 3299 3300 Logically Collective 3301 3302 Input Parameter: 3303 . pc - the preconditioner context 3304 3305 Output Parameter: 3306 . flg - boolean indicating whether to detect fields or not 3307 3308 Options Database Key: 3309 . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point 3310 3311 Level: intermediate 3312 3313 Note: 3314 Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`). 3315 3316 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF` 3317 @*/ 3318 PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg) 3319 { 3320 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3321 3322 PetscFunctionBegin; 3323 jac->detect = flg; 3324 if (jac->detect) { 3325 PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR)); 3326 PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL)); 3327 } 3328 PetscFunctionReturn(PETSC_SUCCESS); 3329 } 3330 3331 /*MC 3332 PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual 3333 collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details. 3334 3335 Options Database Keys: 3336 + -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split 3337 . -pc_fieldsplit_default - automatically add any fields to additional splits that have not 3338 been supplied explicitly by `-pc_fieldsplit_%d_fields` 3339 . -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields) 3340 when the matrix is not of `MatType` `MATNEST` 3341 . -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting 3342 . -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()` 3343 . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`; 3344 see `PCFieldSplitSetSchurFactType()` 3345 . -pc_fieldsplit_dm_splits <true,false> (default is true) - Whether to use `DMCreateFieldDecomposition()` for splits 3346 - -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver 3347 3348 Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` . 3349 The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_` 3350 For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields. 3351 3352 To set options on the solvers for each block append `-fieldsplit_` to all the `PC` 3353 options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1` 3354 3355 To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()` 3356 and set the options directly on the resulting `KSP` object 3357 3358 Level: intermediate 3359 3360 Notes: 3361 Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()` 3362 to define a split by an arbitrary collection of entries. 3363 3364 If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports 3365 `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs, 3366 beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`, 3367 if this is not called the block size defaults to the blocksize of the second matrix passed 3368 to `KSPSetOperators()`/`PCSetOperators()`. 3369 3370 For the Schur complement preconditioner if 3371 ```{math} 3372 J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right] 3373 ``` 3374 3375 the preconditioner using `full` factorization is logically 3376 ```{math} 3377 \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] 3378 ``` 3379 where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`. $S$ is the Schur complement 3380 ```{math} 3381 S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01} 3382 ``` 3383 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 3384 in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0, 3385 it returns the `KSP` associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default 3386 $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$. 3387 3388 The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above, 3389 `diag` gives 3390 ```{math} 3391 \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & -\text{ksp}(S) \end{array}\right] 3392 ``` 3393 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 3394 can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of 3395 ```{math} 3396 \left[\begin{array}{cc} A_{00} & 0 \\ A_{10} & S \end{array}\right] 3397 ``` 3398 where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of 3399 ```{math} 3400 \left[\begin{array}{cc} A_{00} & A_{01} \\ 0 & S \end{array}\right] 3401 ``` 3402 where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s. 3403 3404 If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS` 3405 is used automatically for a second submatrix. 3406 3407 The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1. 3408 Generally it should be used with the `MATAIJ` or `MATNEST` `MatType` 3409 3410 The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see, 3411 for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`. 3412 One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers". 3413 3414 See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`. 3415 3416 The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the 3417 residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables. 3418 3419 The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape 3420 ```{math} 3421 \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right] 3422 ``` 3423 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 $H = _{A00} + \nu*A_{01}*A_{01}'$. 3424 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_`. 3425 3426 Developer Note: 3427 The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their 3428 user API. 3429 3430 .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`, 3431 `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`, 3432 `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`, 3433 `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()` 3434 M*/ 3435 3436 PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc) 3437 { 3438 PC_FieldSplit *jac; 3439 3440 PetscFunctionBegin; 3441 PetscCall(PetscNew(&jac)); 3442 3443 jac->bs = -1; 3444 jac->nsplits = 0; 3445 jac->type = PC_COMPOSITE_MULTIPLICATIVE; 3446 jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */ 3447 jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL; 3448 jac->schurscale = -1.0; 3449 jac->dm_splits = PETSC_TRUE; 3450 jac->detect = PETSC_FALSE; 3451 jac->gkbtol = 1e-5; 3452 jac->gkbdelay = 5; 3453 jac->gkbnu = 1; 3454 jac->gkbmaxit = 100; 3455 jac->gkbmonitor = PETSC_FALSE; 3456 jac->coordinates_set = PETSC_FALSE; 3457 3458 pc->data = (void *)jac; 3459 3460 pc->ops->apply = PCApply_FieldSplit; 3461 pc->ops->applytranspose = PCApplyTranspose_FieldSplit; 3462 pc->ops->setup = PCSetUp_FieldSplit; 3463 pc->ops->reset = PCReset_FieldSplit; 3464 pc->ops->destroy = PCDestroy_FieldSplit; 3465 pc->ops->setfromoptions = PCSetFromOptions_FieldSplit; 3466 pc->ops->view = PCView_FieldSplit; 3467 pc->ops->applyrichardson = NULL; 3468 3469 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit)); 3470 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit)); 3471 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit)); 3472 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit)); 3473 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit)); 3474 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit)); 3475 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit)); 3476 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit)); 3477 PetscFunctionReturn(PETSC_SUCCESS); 3478 } 3479