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 matrix for constructing the preconditioner when solving with S */ 52 Mat schur_user; /* User-provided matrix for constructing the preconditioner for the Schur complement */ 53 PCFieldSplitSchurPreType schurpre; /* Determines which 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 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 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 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 = PETSC_FALSE, issym = PETSC_FALSE, flg; 834 PetscInt rstart, rend; 835 char lscname[256]; 836 PetscObject LSC_L; 837 838 PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields"); 839 840 /* If pc->mat is SPD, don't scale by -1 the Schur complement */ 841 PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd)); 842 if (jac->schurscale == (PetscScalar)-1.0) jac->schurscale = (isset && isspd) ? 1.0 : -1.0; 843 PetscCall(MatIsSymmetricKnown(pc->pmat, &isset, &issym)); 844 845 /* When extracting off-diagonal submatrices, we take complements from this range */ 846 PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend)); 847 PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, "")); 848 849 if (jac->schur) { 850 KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper; 851 MatReuse scall; 852 853 if (pc->flag == DIFFERENT_NONZERO_PATTERN) { 854 scall = MAT_INITIAL_MATRIX; 855 PetscCall(MatDestroy(&jac->B)); 856 PetscCall(MatDestroy(&jac->C)); 857 } else scall = MAT_REUSE_MATRIX; 858 859 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 860 ilink = jac->head; 861 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 862 if (jac->offdiag_use_amat) { 863 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B)); 864 } else { 865 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B)); 866 } 867 PetscCall(ISDestroy(&ccis)); 868 if (!flg) { 869 ilink = ilink->next; 870 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 871 if (jac->offdiag_use_amat) { 872 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C)); 873 } else { 874 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C)); 875 } 876 PetscCall(ISDestroy(&ccis)); 877 } else { 878 PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &isset, &flg)); 879 if (isset && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C)); 880 else PetscCall(MatCreateTranspose(jac->B, &jac->C)); 881 } 882 PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1])); 883 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) { 884 PetscCall(MatDestroy(&jac->schurp)); 885 PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp)); 886 } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL && jac->kspupper != jac->head->ksp) { 887 PetscCall(MatDestroy(&jac->schur_user)); 888 PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 889 } 890 if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0])); 891 if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0])); 892 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac))); 893 } else { 894 const char *Dprefix; 895 char schurprefix[256], schurmatprefix[256]; 896 char schurtestoption[256]; 897 MatNullSpace sp; 898 KSP kspt; 899 900 /* extract the A01 and A10 matrices */ 901 ilink = jac->head; 902 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 903 if (jac->offdiag_use_amat) { 904 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 905 } else { 906 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 907 } 908 PetscCall(ISDestroy(&ccis)); 909 ilink = ilink->next; 910 if (!flg) { 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->C)); 914 } else { 915 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 916 } 917 PetscCall(ISDestroy(&ccis)); 918 } else { 919 PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &isset, &flg)); 920 if (isset && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C)); 921 else PetscCall(MatCreateTranspose(jac->B, &jac->C)); 922 } 923 /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */ 924 PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur)); 925 PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT)); 926 PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1])); 927 PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 928 PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix)); 929 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt)); 930 PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix)); 931 932 /* Note: this is not true in general */ 933 PetscCall(MatGetNullSpace(jac->mat[1], &sp)); 934 if (sp) PetscCall(MatSetNullSpace(jac->schur, sp)); 935 936 PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname)); 937 PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg)); 938 if (flg) { 939 DM dmInner; 940 KSP kspInner; 941 PC pcInner; 942 943 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 944 PetscCall(KSPReset(kspInner)); 945 PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0])); 946 PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 947 /* Indent this deeper to emphasize the "inner" nature of this solver. */ 948 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2)); 949 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2)); 950 PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix)); 951 952 /* Set DM for new solver */ 953 PetscCall(KSPGetDM(jac->head->ksp, &dmInner)); 954 PetscCall(KSPSetDM(kspInner, dmInner)); 955 PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE)); 956 957 /* Defaults to PCKSP as preconditioner */ 958 PetscCall(KSPGetPC(kspInner, &pcInner)); 959 PetscCall(PCSetType(pcInner, PCKSP)); 960 PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp)); 961 } else { 962 /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or 963 * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact, 964 * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for 965 * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make 966 * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used 967 * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */ 968 PetscCall(KSPSetType(jac->head->ksp, KSPGMRES)); 969 PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp)); 970 } 971 PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0])); 972 PetscCall(KSPSetFromOptions(jac->head->ksp)); 973 PetscCall(MatSetFromOptions(jac->schur)); 974 975 PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg)); 976 if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */ 977 KSP kspInner; 978 PC pcInner; 979 980 PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner)); 981 PetscCall(KSPGetPC(kspInner, &pcInner)); 982 PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg)); 983 if (flg) { 984 KSP ksp; 985 986 PetscCall(PCKSPGetKSP(pcInner, &ksp)); 987 if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE)); 988 } 989 } 990 PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname)); 991 PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg)); 992 if (flg) { 993 DM dmInner; 994 995 PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 996 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper)); 997 PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel)); 998 PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure)); 999 PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix)); 1000 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1)); 1001 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1)); 1002 PetscCall(KSPGetDM(jac->head->ksp, &dmInner)); 1003 PetscCall(KSPSetDM(jac->kspupper, dmInner)); 1004 PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE)); 1005 PetscCall(KSPSetFromOptions(jac->kspupper)); 1006 PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0])); 1007 PetscCall(VecDuplicate(jac->head->x, &jac->head->z)); 1008 } else { 1009 jac->kspupper = jac->head->ksp; 1010 PetscCall(PetscObjectReference((PetscObject)jac->head->ksp)); 1011 } 1012 1013 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp)); 1014 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur)); 1015 PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel)); 1016 PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure)); 1017 PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1)); 1018 if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) { 1019 PC pcschur; 1020 PetscCall(KSPGetPC(jac->kspschur, &pcschur)); 1021 PetscCall(PCSetType(pcschur, PCNONE)); 1022 /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */ 1023 } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) { 1024 if (jac->schurfactorization != PC_FIELDSPLIT_SCHUR_FACT_FULL || jac->kspupper != jac->head->ksp) PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 1025 } 1026 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac))); 1027 PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix)); 1028 PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix)); 1029 /* propagate DM */ 1030 { 1031 DM sdm; 1032 PetscCall(KSPGetDM(jac->head->next->ksp, &sdm)); 1033 if (sdm) { 1034 PetscCall(KSPSetDM(jac->kspschur, sdm)); 1035 PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE)); 1036 } 1037 } 1038 /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */ 1039 /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */ 1040 PetscCall(KSPSetFromOptions(jac->kspschur)); 1041 } 1042 PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY)); 1043 PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY)); 1044 if (issym) PetscCall(MatSetOption(jac->schur, MAT_SYMMETRIC, PETSC_TRUE)); 1045 if (isspd) PetscCall(MatSetOption(jac->schur, MAT_SPD, PETSC_TRUE)); 1046 1047 /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */ 1048 PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname)); 1049 PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L)); 1050 if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L)); 1051 if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", LSC_L)); 1052 PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname)); 1053 PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L)); 1054 if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L)); 1055 if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", LSC_L)); 1056 } else if (jac->type == PC_COMPOSITE_GKB) { 1057 IS ccis; 1058 PetscInt rstart, rend; 1059 1060 PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields"); 1061 1062 ilink = jac->head; 1063 1064 /* When extracting off-diagonal submatrices, we take complements from this range */ 1065 PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend)); 1066 1067 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 1068 if (jac->offdiag_use_amat) { 1069 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 1070 } else { 1071 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B)); 1072 } 1073 PetscCall(ISDestroy(&ccis)); 1074 /* Create work vectors for GKB algorithm */ 1075 PetscCall(VecDuplicate(ilink->x, &jac->u)); 1076 PetscCall(VecDuplicate(ilink->x, &jac->Hu)); 1077 PetscCall(VecDuplicate(ilink->x, &jac->w2)); 1078 ilink = ilink->next; 1079 PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis)); 1080 if (jac->offdiag_use_amat) { 1081 PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 1082 } else { 1083 PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C)); 1084 } 1085 PetscCall(ISDestroy(&ccis)); 1086 /* Create work vectors for GKB algorithm */ 1087 PetscCall(VecDuplicate(ilink->x, &jac->v)); 1088 PetscCall(VecDuplicate(ilink->x, &jac->d)); 1089 PetscCall(VecDuplicate(ilink->x, &jac->w1)); 1090 PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu)); 1091 PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz)); 1092 1093 ilink = jac->head; 1094 PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H)); 1095 if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp)); 1096 /* Create gkb_monitor context */ 1097 if (jac->gkbmonitor) { 1098 PetscInt tablevel; 1099 PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer)); 1100 PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII)); 1101 PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel)); 1102 PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel)); 1103 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1)); 1104 } 1105 } else { 1106 /* set up the individual splits' PCs */ 1107 i = 0; 1108 ilink = jac->head; 1109 while (ilink) { 1110 PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i])); 1111 /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */ 1112 if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp)); 1113 i++; 1114 ilink = ilink->next; 1115 } 1116 } 1117 1118 /* Set coordinates to the sub PC objects whenever these are set */ 1119 if (jac->coordinates_set) { 1120 PC pc_coords; 1121 if (jac->type == PC_COMPOSITE_SCHUR) { 1122 // Head is first block. 1123 PetscCall(KSPGetPC(jac->head->ksp, &pc_coords)); 1124 PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords)); 1125 // Second one is Schur block, but its KSP object is in kspschur. 1126 PetscCall(KSPGetPC(jac->kspschur, &pc_coords)); 1127 PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords)); 1128 } else if (jac->type == PC_COMPOSITE_GKB) { 1129 PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n")); 1130 } else { 1131 ilink = jac->head; 1132 while (ilink) { 1133 PetscCall(KSPGetPC(ilink->ksp, &pc_coords)); 1134 PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords)); 1135 ilink = ilink->next; 1136 } 1137 } 1138 } 1139 1140 jac->suboptionsset = PETSC_TRUE; 1141 PetscFunctionReturn(PETSC_SUCCESS); 1142 } 1143 1144 static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc) 1145 { 1146 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1147 PC_FieldSplitLink ilinkA = jac->head; 1148 KSP kspA = ilinkA->ksp, kspUpper = jac->kspupper; 1149 1150 PetscFunctionBegin; 1151 if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) { 1152 PetscCall(KSPSetUp(kspUpper)); 1153 PetscCall(KSPSetUpOnBlocks(kspUpper)); 1154 } 1155 PetscCall(KSPSetUp(kspA)); 1156 PetscCall(KSPSetUpOnBlocks(kspA)); 1157 if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) { 1158 PetscCall(KSPSetUp(jac->kspschur)); 1159 PetscCall(KSPSetUpOnBlocks(jac->kspschur)); 1160 } else if (kspUpper == kspA) { 1161 Mat A; 1162 PetscInt m, M, N; 1163 VecType vtype; 1164 PetscMemType mtype; 1165 PetscScalar *array; 1166 1167 PetscCall(MatGetSize(jac->B, &M, &N)); 1168 PetscCall(MatGetLocalSize(jac->B, &m, NULL)); 1169 PetscCall(MatGetVecType(jac->B, &vtype)); 1170 PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype)); 1171 PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array)); 1172 if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array)); 1173 #if PetscDefined(HAVE_CUDA) 1174 else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1))); 1175 #endif 1176 #if PetscDefined(HAVE_HIP) 1177 else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1))); 1178 #endif 1179 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 1180 PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)A)); 1181 PetscCall(MatDestroy(&A)); 1182 } 1183 PetscFunctionReturn(PETSC_SUCCESS); 1184 } 1185 1186 static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc) 1187 { 1188 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1189 PC_FieldSplitLink ilink = jac->head; 1190 1191 PetscFunctionBegin; 1192 while (ilink) { 1193 PetscCall(KSPSetUp(ilink->ksp)); 1194 PetscCall(KSPSetUpOnBlocks(ilink->ksp)); 1195 ilink = ilink->next; 1196 } 1197 PetscFunctionReturn(PETSC_SUCCESS); 1198 } 1199 1200 static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc) 1201 { 1202 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1203 PC_FieldSplitLink ilinkA = jac->head; 1204 KSP ksp = ilinkA->ksp; 1205 1206 PetscFunctionBegin; 1207 PetscCall(KSPSetUp(ksp)); 1208 PetscCall(KSPSetUpOnBlocks(ksp)); 1209 PetscFunctionReturn(PETSC_SUCCESS); 1210 } 1211 1212 static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y) 1213 { 1214 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1215 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1216 KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper; 1217 Mat AinvB = NULL; 1218 PetscInt N, P; 1219 1220 PetscFunctionBegin; 1221 switch (jac->schurfactorization) { 1222 case PC_FIELDSPLIT_SCHUR_FACT_DIAG: 1223 /* [A00 0; 0 -S], positive definite, suitable for MINRES */ 1224 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1225 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1226 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1227 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1228 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1229 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1230 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1231 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1232 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1233 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1234 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1235 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1236 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1237 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1238 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1239 PetscCall(VecScale(ilinkD->y, jac->schurscale)); 1240 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1241 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1242 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1243 break; 1244 case PC_FIELDSPLIT_SCHUR_FACT_LOWER: 1245 /* [A00 0; A10 S], suitable for left preconditioning */ 1246 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1247 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1248 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1249 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1250 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1251 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1252 PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x)); 1253 PetscCall(VecScale(ilinkD->x, -1.)); 1254 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1255 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1256 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1257 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1258 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1259 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1260 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1261 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1262 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1263 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1264 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1265 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1266 break; 1267 case PC_FIELDSPLIT_SCHUR_FACT_UPPER: 1268 /* [A00 A01; 0 S], suitable for right preconditioning */ 1269 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1270 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1271 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1272 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1273 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1274 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1275 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1276 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1277 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x)); 1278 PetscCall(VecScale(ilinkA->x, -1.)); 1279 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1280 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1281 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1282 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1283 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1284 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1285 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1286 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1287 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1288 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1289 break; 1290 case PC_FIELDSPLIT_SCHUR_FACT_FULL: 1291 /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */ 1292 PetscCall(MatGetSize(jac->B, NULL, &P)); 1293 N = P; 1294 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1295 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1296 PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL)); 1297 if (kspUpper == kspA) { 1298 PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB)); 1299 if (AinvB) { 1300 PetscCall(MatGetSize(AinvB, NULL, &N)); 1301 if (N > P) { // first time PCApply_FieldSplit_Schur() is called 1302 PetscMemType mtype; 1303 Vec c = NULL; 1304 PetscScalar *array; 1305 PetscInt m, M; 1306 1307 PetscCall(MatGetSize(jac->B, &M, NULL)); 1308 PetscCall(MatGetLocalSize(jac->B, &m, NULL)); 1309 PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype)); 1310 if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1311 #if PetscDefined(HAVE_CUDA) 1312 else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1313 #endif 1314 #if PetscDefined(HAVE_HIP) 1315 else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c)); 1316 #endif 1317 PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array)); 1318 PetscCall(VecCopy(ilinkA->x, c)); 1319 PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user)); 1320 PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user)); 1321 PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat 1322 PetscCall(VecDestroy(&c)); 1323 } 1324 } 1325 } 1326 if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y)); 1327 PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y)); 1328 PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL)); 1329 PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x)); 1330 PetscCall(VecScale(ilinkD->x, -1.0)); 1331 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1332 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1333 1334 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1335 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1336 PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y)); 1337 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1338 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1339 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1340 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1341 1342 if (kspUpper == kspA) { 1343 if (!AinvB) { 1344 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y)); 1345 PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y)); 1346 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1347 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1348 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1349 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1350 } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y)); 1351 } else { 1352 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1353 PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y)); 1354 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1355 PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x)); 1356 PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL)); 1357 PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z)); 1358 PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z)); 1359 PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL)); 1360 PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z)); 1361 } 1362 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1363 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1364 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1365 } 1366 PetscFunctionReturn(PETSC_SUCCESS); 1367 } 1368 1369 static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y) 1370 { 1371 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1372 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1373 KSP kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper; 1374 1375 PetscFunctionBegin; 1376 switch (jac->schurfactorization) { 1377 case PC_FIELDSPLIT_SCHUR_FACT_DIAG: 1378 /* [A00 0; 0 -S], positive definite, suitable for MINRES */ 1379 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1380 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1381 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1382 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1383 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1384 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1385 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1386 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1387 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1388 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1389 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1390 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1391 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1392 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1393 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1394 PetscCall(VecScale(ilinkD->y, jac->schurscale)); 1395 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1396 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1397 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1398 break; 1399 case PC_FIELDSPLIT_SCHUR_FACT_UPPER: 1400 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1401 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1402 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1403 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1404 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1405 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1406 PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x)); 1407 PetscCall(VecScale(ilinkD->x, -1.)); 1408 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1409 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1410 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1411 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1412 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1413 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1414 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1415 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1416 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1417 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1418 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1419 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1420 break; 1421 case PC_FIELDSPLIT_SCHUR_FACT_LOWER: 1422 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1423 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1424 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1425 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1426 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1427 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1428 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1429 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1430 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x)); 1431 PetscCall(VecScale(ilinkA->x, -1.)); 1432 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1433 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1434 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD)); 1435 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1436 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1437 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1438 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1439 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1440 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1441 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1442 break; 1443 case PC_FIELDSPLIT_SCHUR_FACT_FULL: 1444 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1445 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1446 PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL)); 1447 PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y)); 1448 PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y)); 1449 PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL)); 1450 PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x)); 1451 PetscCall(VecScale(ilinkD->x, -1.0)); 1452 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1453 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD)); 1454 1455 PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1456 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1)); 1457 PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y)); 1458 PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1)); 1459 PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y)); 1460 PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL)); 1461 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1462 1463 if (kspLower == kspA) { 1464 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y)); 1465 PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y)); 1466 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1467 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1468 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1469 PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1470 } else { 1471 PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL)); 1472 PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y)); 1473 PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y)); 1474 PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x)); 1475 PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL)); 1476 PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z)); 1477 PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z)); 1478 PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL)); 1479 PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z)); 1480 } 1481 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1482 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1483 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1484 } 1485 PetscFunctionReturn(PETSC_SUCCESS); 1486 } 1487 1488 #define FieldSplitSplitSolveAdd(ilink, xx, yy) \ 1489 ((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) || \ 1490 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) || \ 1491 VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE))) 1492 1493 static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y) 1494 { 1495 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1496 PC_FieldSplitLink ilink = jac->head; 1497 PetscInt cnt, bs; 1498 1499 PetscFunctionBegin; 1500 if (jac->type == PC_COMPOSITE_ADDITIVE) { 1501 PetscBool matnest; 1502 1503 PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest)); 1504 if (jac->defaultsplit && !matnest) { 1505 PetscCall(VecGetBlockSize(x, &bs)); 1506 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); 1507 PetscCall(VecGetBlockSize(y, &bs)); 1508 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); 1509 PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES)); 1510 while (ilink) { 1511 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1512 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1513 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1514 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1515 ilink = ilink->next; 1516 } 1517 PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES)); 1518 } else { 1519 PetscCall(VecSet(y, 0.0)); 1520 while (ilink) { 1521 PetscCall(FieldSplitSplitSolveAdd(ilink, x, y)); 1522 ilink = ilink->next; 1523 } 1524 } 1525 } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) { 1526 PetscCall(VecSet(y, 0.0)); 1527 /* solve on first block for first block variables */ 1528 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD)); 1529 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD)); 1530 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1531 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1532 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1533 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1534 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1535 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1536 1537 /* compute the residual only onto second block variables using first block variables */ 1538 PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x)); 1539 ilink = ilink->next; 1540 PetscCall(VecScale(ilink->x, -1.0)); 1541 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1542 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1543 1544 /* solve on second block variables */ 1545 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1546 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1547 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1548 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1549 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1550 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1551 } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1552 if (!jac->w1) { 1553 PetscCall(VecDuplicate(x, &jac->w1)); 1554 PetscCall(VecDuplicate(x, &jac->w2)); 1555 } 1556 PetscCall(VecSet(y, 0.0)); 1557 PetscCall(FieldSplitSplitSolveAdd(ilink, x, y)); 1558 cnt = 1; 1559 while (ilink->next) { 1560 ilink = ilink->next; 1561 /* compute the residual only over the part of the vector needed */ 1562 PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x)); 1563 PetscCall(VecScale(ilink->x, -1.0)); 1564 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1565 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1566 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1567 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1568 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1569 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1570 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1571 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1572 } 1573 if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1574 cnt -= 2; 1575 while (ilink->previous) { 1576 ilink = ilink->previous; 1577 /* compute the residual only over the part of the vector needed */ 1578 PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x)); 1579 PetscCall(VecScale(ilink->x, -1.0)); 1580 PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1581 PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD)); 1582 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1583 PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y)); 1584 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1585 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1586 PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1587 PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE)); 1588 } 1589 } 1590 } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type); 1591 PetscFunctionReturn(PETSC_SUCCESS); 1592 } 1593 1594 static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y) 1595 { 1596 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1597 PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next; 1598 KSP ksp = ilinkA->ksp; 1599 Vec u, v, Hu, d, work1, work2; 1600 PetscScalar alpha, z, nrmz2, *vecz; 1601 PetscReal lowbnd, nu, beta; 1602 PetscInt j, iterGKB; 1603 1604 PetscFunctionBegin; 1605 PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1606 PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1607 PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD)); 1608 PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD)); 1609 1610 u = jac->u; 1611 v = jac->v; 1612 Hu = jac->Hu; 1613 d = jac->d; 1614 work1 = jac->w1; 1615 work2 = jac->w2; 1616 vecz = jac->vecz; 1617 1618 /* Change RHS to comply with matrix regularization H = A + nu*B*B' */ 1619 /* Add q = q + nu*B*b */ 1620 if (jac->gkbnu) { 1621 nu = jac->gkbnu; 1622 PetscCall(VecScale(ilinkD->x, jac->gkbnu)); 1623 PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */ 1624 } else { 1625 /* Situation when no augmented Lagrangian is used. Then we set inner */ 1626 /* matrix N = I in [Ar13], and thus nu = 1. */ 1627 nu = 1; 1628 } 1629 1630 /* Transform rhs from [q,tilde{b}] to [0,b] */ 1631 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL)); 1632 PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y)); 1633 PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y)); 1634 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL)); 1635 PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1)); 1636 PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x */ 1637 1638 /* First step of algorithm */ 1639 PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/ 1640 KSPCheckDot(ksp, beta); 1641 beta = PetscSqrtReal(nu) * beta; 1642 PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c */ 1643 PetscCall(MatMult(jac->B, v, work2)); /* u = H^{-1}*B*v */ 1644 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL)); 1645 PetscCall(KSPSolve(ksp, work2, u)); 1646 PetscCall(KSPCheckSolve(ksp, pc, u)); 1647 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL)); 1648 PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */ 1649 PetscCall(VecDot(Hu, u, &alpha)); 1650 KSPCheckDot(ksp, alpha); 1651 PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite"); 1652 alpha = PetscSqrtReal(PetscAbsScalar(alpha)); 1653 PetscCall(VecScale(u, 1.0 / alpha)); 1654 PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c */ 1655 1656 z = beta / alpha; 1657 vecz[1] = z; 1658 1659 /* Computation of first iterate x(1) and p(1) */ 1660 PetscCall(VecAXPY(ilinkA->y, z, u)); 1661 PetscCall(VecCopy(d, ilinkD->y)); 1662 PetscCall(VecScale(ilinkD->y, -z)); 1663 1664 iterGKB = 1; 1665 lowbnd = 2 * jac->gkbtol; 1666 if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd)); 1667 1668 while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) { 1669 iterGKB += 1; 1670 PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */ 1671 PetscCall(VecAXPBY(v, nu, -alpha, work1)); 1672 PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v */ 1673 beta = beta / PetscSqrtReal(nu); 1674 PetscCall(VecScale(v, 1.0 / beta)); 1675 PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */ 1676 PetscCall(MatMult(jac->H, u, Hu)); 1677 PetscCall(VecAXPY(work2, -beta, Hu)); 1678 PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL)); 1679 PetscCall(KSPSolve(ksp, work2, u)); 1680 PetscCall(KSPCheckSolve(ksp, pc, u)); 1681 PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL)); 1682 PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u */ 1683 PetscCall(VecDot(Hu, u, &alpha)); 1684 KSPCheckDot(ksp, alpha); 1685 PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite"); 1686 alpha = PetscSqrtReal(PetscAbsScalar(alpha)); 1687 PetscCall(VecScale(u, 1.0 / alpha)); 1688 1689 z = -beta / alpha * z; /* z <- beta/alpha*z */ 1690 vecz[0] = z; 1691 1692 /* Computation of new iterate x(i+1) and p(i+1) */ 1693 PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */ 1694 PetscCall(VecAXPY(ilinkA->y, z, u)); /* r = r + z*u */ 1695 PetscCall(VecAXPY(ilinkD->y, -z, d)); /* p = p - z*d */ 1696 PetscCall(MatMult(jac->H, ilinkA->y, Hu)); /* ||u||_H = u'*H*u */ 1697 PetscCall(VecDot(Hu, ilinkA->y, &nrmz2)); 1698 1699 /* Compute Lower Bound estimate */ 1700 if (iterGKB > jac->gkbdelay) { 1701 lowbnd = 0.0; 1702 for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]); 1703 lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2)); 1704 } 1705 1706 for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2]; 1707 if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd)); 1708 } 1709 1710 PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1711 PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1712 PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1713 PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE)); 1714 PetscFunctionReturn(PETSC_SUCCESS); 1715 } 1716 1717 #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \ 1718 ((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) || \ 1719 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) || \ 1720 VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE))) 1721 1722 static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y) 1723 { 1724 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1725 PC_FieldSplitLink ilink = jac->head; 1726 PetscInt bs; 1727 1728 PetscFunctionBegin; 1729 if (jac->type == PC_COMPOSITE_ADDITIVE) { 1730 PetscBool matnest; 1731 1732 PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest)); 1733 if (jac->defaultsplit && !matnest) { 1734 PetscCall(VecGetBlockSize(x, &bs)); 1735 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); 1736 PetscCall(VecGetBlockSize(y, &bs)); 1737 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); 1738 PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES)); 1739 while (ilink) { 1740 PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1741 PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y)); 1742 PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y)); 1743 PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL)); 1744 ilink = ilink->next; 1745 } 1746 PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES)); 1747 } else { 1748 PetscCall(VecSet(y, 0.0)); 1749 while (ilink) { 1750 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1751 ilink = ilink->next; 1752 } 1753 } 1754 } else { 1755 if (!jac->w1) { 1756 PetscCall(VecDuplicate(x, &jac->w1)); 1757 PetscCall(VecDuplicate(x, &jac->w2)); 1758 } 1759 PetscCall(VecSet(y, 0.0)); 1760 if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) { 1761 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1762 while (ilink->next) { 1763 ilink = ilink->next; 1764 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1765 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1766 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1767 } 1768 while (ilink->previous) { 1769 ilink = ilink->previous; 1770 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1771 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1772 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1773 } 1774 } else { 1775 while (ilink->next) { /* get to last entry in linked list */ 1776 ilink = ilink->next; 1777 } 1778 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y)); 1779 while (ilink->previous) { 1780 ilink = ilink->previous; 1781 PetscCall(MatMultTranspose(pc->mat, y, jac->w1)); 1782 PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x)); 1783 PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y)); 1784 } 1785 } 1786 } 1787 PetscFunctionReturn(PETSC_SUCCESS); 1788 } 1789 1790 static PetscErrorCode PCReset_FieldSplit(PC pc) 1791 { 1792 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1793 PC_FieldSplitLink ilink = jac->head, next; 1794 1795 PetscFunctionBegin; 1796 while (ilink) { 1797 PetscCall(KSPDestroy(&ilink->ksp)); 1798 PetscCall(VecDestroy(&ilink->x)); 1799 PetscCall(VecDestroy(&ilink->y)); 1800 PetscCall(VecDestroy(&ilink->z)); 1801 PetscCall(VecScatterDestroy(&ilink->sctx)); 1802 PetscCall(ISDestroy(&ilink->is)); 1803 PetscCall(ISDestroy(&ilink->is_col)); 1804 PetscCall(PetscFree(ilink->splitname)); 1805 PetscCall(PetscFree(ilink->fields)); 1806 PetscCall(PetscFree(ilink->fields_col)); 1807 next = ilink->next; 1808 PetscCall(PetscFree(ilink)); 1809 ilink = next; 1810 } 1811 jac->head = NULL; 1812 PetscCall(PetscFree2(jac->x, jac->y)); 1813 if (jac->mat && jac->mat != jac->pmat) { 1814 PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat)); 1815 } else if (jac->mat) { 1816 jac->mat = NULL; 1817 } 1818 if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat)); 1819 if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield)); 1820 jac->nsplits = 0; 1821 PetscCall(VecDestroy(&jac->w1)); 1822 PetscCall(VecDestroy(&jac->w2)); 1823 if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL)); 1824 PetscCall(MatDestroy(&jac->schur)); 1825 PetscCall(MatDestroy(&jac->schurp)); 1826 PetscCall(MatDestroy(&jac->schur_user)); 1827 PetscCall(KSPDestroy(&jac->kspschur)); 1828 PetscCall(KSPDestroy(&jac->kspupper)); 1829 PetscCall(MatDestroy(&jac->B)); 1830 PetscCall(MatDestroy(&jac->C)); 1831 PetscCall(MatDestroy(&jac->H)); 1832 PetscCall(VecDestroy(&jac->u)); 1833 PetscCall(VecDestroy(&jac->v)); 1834 PetscCall(VecDestroy(&jac->Hu)); 1835 PetscCall(VecDestroy(&jac->d)); 1836 PetscCall(PetscFree(jac->vecz)); 1837 PetscCall(PetscViewerDestroy(&jac->gkbviewer)); 1838 jac->isrestrict = PETSC_FALSE; 1839 PetscFunctionReturn(PETSC_SUCCESS); 1840 } 1841 1842 static PetscErrorCode PCDestroy_FieldSplit(PC pc) 1843 { 1844 PetscFunctionBegin; 1845 PetscCall(PCReset_FieldSplit(pc)); 1846 PetscCall(PetscFree(pc->data)); 1847 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL)); 1848 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL)); 1849 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL)); 1850 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL)); 1851 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL)); 1852 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL)); 1853 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL)); 1854 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL)); 1855 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL)); 1856 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL)); 1857 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL)); 1858 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL)); 1859 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL)); 1860 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL)); 1861 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL)); 1862 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL)); 1863 PetscFunctionReturn(PETSC_SUCCESS); 1864 } 1865 1866 static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems PetscOptionsObject) 1867 { 1868 PetscInt bs; 1869 PetscBool flg; 1870 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1871 PCCompositeType ctype; 1872 1873 PetscFunctionBegin; 1874 PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options"); 1875 PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL)); 1876 PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg)); 1877 if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs)); 1878 jac->diag_use_amat = pc->useAmat; 1879 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)); 1880 jac->offdiag_use_amat = pc->useAmat; 1881 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)); 1882 PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL)); 1883 PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */ 1884 PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg)); 1885 if (flg) PetscCall(PCFieldSplitSetType(pc, ctype)); 1886 /* Only setup fields once */ 1887 if ((jac->bs > 0) && (jac->nsplits == 0)) { 1888 /* only allow user to set fields from command line. 1889 otherwise user can set them in PCFieldSplitSetDefaults() */ 1890 PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc)); 1891 if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n")); 1892 } 1893 if (jac->type == PC_COMPOSITE_SCHUR) { 1894 PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg)); 1895 if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n")); 1896 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)); 1897 PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL)); 1898 PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL)); 1899 } else if (jac->type == PC_COMPOSITE_GKB) { 1900 PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL)); 1901 PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL)); 1902 PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0)); 1903 PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL)); 1904 PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL)); 1905 } 1906 /* 1907 In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet. 1908 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 1909 is called on the outer solver in case changes were made in the options database 1910 1911 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() 1912 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. 1913 Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types. 1914 1915 There could be a negative side effect of calling the KSPSetFromOptions() below. 1916 1917 If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call 1918 */ 1919 if (jac->issetup) { 1920 PC_FieldSplitLink ilink = jac->head; 1921 if (jac->type == PC_COMPOSITE_SCHUR) { 1922 if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper)); 1923 if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur)); 1924 } 1925 while (ilink) { 1926 if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp)); 1927 ilink = ilink->next; 1928 } 1929 } 1930 PetscOptionsHeadEnd(); 1931 PetscFunctionReturn(PETSC_SUCCESS); 1932 } 1933 1934 static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col) 1935 { 1936 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1937 PC_FieldSplitLink ilink, next = jac->head; 1938 char prefix[128]; 1939 PetscInt i; 1940 PetscLogEvent nse; 1941 1942 PetscFunctionBegin; 1943 if (jac->splitdefined) { 1944 PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname)); 1945 PetscFunctionReturn(PETSC_SUCCESS); 1946 } 1947 for (i = 0; i < n; i++) { PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]); } 1948 PetscCall(PetscNew(&ilink)); 1949 if (splitname) { 1950 PetscCall(PetscStrallocpy(splitname, &ilink->splitname)); 1951 } else { 1952 PetscCall(PetscMalloc1(3, &ilink->splitname)); 1953 PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits)); 1954 } 1955 PetscCall(PetscMPIIntCast(jac->nsplits, &nse)); 1956 ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */ 1957 PetscCall(PetscMalloc1(n, &ilink->fields)); 1958 PetscCall(PetscArraycpy(ilink->fields, fields, n)); 1959 PetscCall(PetscMalloc1(n, &ilink->fields_col)); 1960 PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n)); 1961 1962 ilink->nfields = n; 1963 ilink->next = NULL; 1964 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp)); 1965 PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel)); 1966 PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure)); 1967 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1)); 1968 PetscCall(KSPSetType(ilink->ksp, KSPPREONLY)); 1969 1970 PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 1971 PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix)); 1972 1973 if (!next) { 1974 jac->head = ilink; 1975 ilink->previous = NULL; 1976 } else { 1977 while (next->next) next = next->next; 1978 next->next = ilink; 1979 ilink->previous = next; 1980 } 1981 jac->nsplits++; 1982 PetscFunctionReturn(PETSC_SUCCESS); 1983 } 1984 1985 static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp) 1986 { 1987 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 1988 1989 PetscFunctionBegin; 1990 *subksp = NULL; 1991 if (n) *n = 0; 1992 if (jac->type == PC_COMPOSITE_SCHUR) { 1993 PetscInt nn; 1994 1995 PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()"); 1996 PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits); 1997 nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0); 1998 PetscCall(PetscMalloc1(nn, subksp)); 1999 (*subksp)[0] = jac->head->ksp; 2000 (*subksp)[1] = jac->kspschur; 2001 if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper; 2002 if (n) *n = nn; 2003 } 2004 PetscFunctionReturn(PETSC_SUCCESS); 2005 } 2006 2007 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp) 2008 { 2009 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2010 2011 PetscFunctionBegin; 2012 PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()"); 2013 PetscCall(PetscMalloc1(jac->nsplits, subksp)); 2014 PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp)); 2015 2016 (*subksp)[1] = jac->kspschur; 2017 if (n) *n = jac->nsplits; 2018 PetscFunctionReturn(PETSC_SUCCESS); 2019 } 2020 2021 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp) 2022 { 2023 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2024 PetscInt cnt = 0; 2025 PC_FieldSplitLink ilink = jac->head; 2026 2027 PetscFunctionBegin; 2028 PetscCall(PetscMalloc1(jac->nsplits, subksp)); 2029 while (ilink) { 2030 (*subksp)[cnt++] = ilink->ksp; 2031 ilink = ilink->next; 2032 } 2033 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); 2034 if (n) *n = jac->nsplits; 2035 PetscFunctionReturn(PETSC_SUCCESS); 2036 } 2037 2038 /*@ 2039 PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`. 2040 2041 Input Parameters: 2042 + pc - the preconditioner context 2043 - isy - the index set that defines the indices to which the fieldsplit is to be restricted 2044 2045 Level: advanced 2046 2047 Developer Notes: 2048 It seems the resulting `IS`s will not cover the entire space, so 2049 how can they define a convergent preconditioner? Needs explaining. 2050 2051 .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 2052 @*/ 2053 PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy) 2054 { 2055 PetscFunctionBegin; 2056 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2057 PetscValidHeaderSpecific(isy, IS_CLASSID, 2); 2058 PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy)); 2059 PetscFunctionReturn(PETSC_SUCCESS); 2060 } 2061 2062 static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy) 2063 { 2064 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2065 PC_FieldSplitLink ilink = jac->head, next; 2066 PetscInt localsize, size, sizez, i; 2067 const PetscInt *ind, *indz; 2068 PetscInt *indc, *indcz; 2069 PetscBool flg; 2070 2071 PetscFunctionBegin; 2072 PetscCall(ISGetLocalSize(isy, &localsize)); 2073 PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy))); 2074 size -= localsize; 2075 while (ilink) { 2076 IS isrl, isr; 2077 PC subpc; 2078 PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl)); 2079 PetscCall(ISGetLocalSize(isrl, &localsize)); 2080 PetscCall(PetscMalloc1(localsize, &indc)); 2081 PetscCall(ISGetIndices(isrl, &ind)); 2082 PetscCall(PetscArraycpy(indc, ind, localsize)); 2083 PetscCall(ISRestoreIndices(isrl, &ind)); 2084 PetscCall(ISDestroy(&isrl)); 2085 for (i = 0; i < localsize; i++) *(indc + i) += size; 2086 PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr)); 2087 PetscCall(PetscObjectReference((PetscObject)isr)); 2088 PetscCall(ISDestroy(&ilink->is)); 2089 ilink->is = isr; 2090 PetscCall(PetscObjectReference((PetscObject)isr)); 2091 PetscCall(ISDestroy(&ilink->is_col)); 2092 ilink->is_col = isr; 2093 PetscCall(ISDestroy(&isr)); 2094 PetscCall(KSPGetPC(ilink->ksp, &subpc)); 2095 PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg)); 2096 if (flg) { 2097 IS iszl, isz; 2098 MPI_Comm comm; 2099 PetscCall(ISGetLocalSize(ilink->is, &localsize)); 2100 comm = PetscObjectComm((PetscObject)ilink->is); 2101 PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl)); 2102 PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm)); 2103 sizez -= localsize; 2104 PetscCall(ISGetLocalSize(iszl, &localsize)); 2105 PetscCall(PetscMalloc1(localsize, &indcz)); 2106 PetscCall(ISGetIndices(iszl, &indz)); 2107 PetscCall(PetscArraycpy(indcz, indz, localsize)); 2108 PetscCall(ISRestoreIndices(iszl, &indz)); 2109 PetscCall(ISDestroy(&iszl)); 2110 for (i = 0; i < localsize; i++) *(indcz + i) += sizez; 2111 PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz)); 2112 PetscCall(PCFieldSplitRestrictIS(subpc, isz)); 2113 PetscCall(ISDestroy(&isz)); 2114 } 2115 next = ilink->next; 2116 ilink = next; 2117 } 2118 jac->isrestrict = PETSC_TRUE; 2119 PetscFunctionReturn(PETSC_SUCCESS); 2120 } 2121 2122 static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is) 2123 { 2124 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2125 PC_FieldSplitLink ilink, next = jac->head; 2126 char prefix[128]; 2127 PetscLogEvent nse; 2128 2129 PetscFunctionBegin; 2130 if (jac->splitdefined) { 2131 PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname)); 2132 PetscFunctionReturn(PETSC_SUCCESS); 2133 } 2134 PetscCall(PetscNew(&ilink)); 2135 if (splitname) { 2136 PetscCall(PetscStrallocpy(splitname, &ilink->splitname)); 2137 } else { 2138 PetscCall(PetscMalloc1(8, &ilink->splitname)); 2139 PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits)); 2140 } 2141 PetscCall(PetscMPIIntCast(jac->nsplits, &nse)); 2142 ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */ 2143 PetscCall(PetscObjectReference((PetscObject)is)); 2144 PetscCall(ISDestroy(&ilink->is)); 2145 ilink->is = is; 2146 PetscCall(PetscObjectReference((PetscObject)is)); 2147 PetscCall(ISDestroy(&ilink->is_col)); 2148 ilink->is_col = is; 2149 ilink->next = NULL; 2150 PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp)); 2151 PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel)); 2152 PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure)); 2153 PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1)); 2154 PetscCall(KSPSetType(ilink->ksp, KSPPREONLY)); 2155 2156 PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname)); 2157 PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix)); 2158 2159 if (!next) { 2160 jac->head = ilink; 2161 ilink->previous = NULL; 2162 } else { 2163 while (next->next) next = next->next; 2164 next->next = ilink; 2165 ilink->previous = next; 2166 } 2167 jac->nsplits++; 2168 PetscFunctionReturn(PETSC_SUCCESS); 2169 } 2170 2171 /*@ 2172 PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT` 2173 2174 Logically Collective 2175 2176 Input Parameters: 2177 + pc - the preconditioner context 2178 . splitname - name of this split, if `NULL` the number of the split is used 2179 . n - the number of fields in this split 2180 . fields - the fields in this split 2181 - 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 2182 of the matrix and `fields_col` provides the column indices for that block 2183 2184 Options Database Key: 2185 . -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split 2186 2187 Level: intermediate 2188 2189 Notes: 2190 Use `PCFieldSplitSetIS()` to set a general set of indices as a split. 2191 2192 If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`. 2193 2194 If the matrix used to construct the preconditioner is not `MATNEST` then 2195 `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlockSize()` or 2196 to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block 2197 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 2198 0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x23x56x8.. x12x45x78x.... 2199 where the numbered entries indicate what is in the split. 2200 2201 This function is called once per split (it creates a new split each time). Solve options 2202 for this split will be available under the prefix `-fieldsplit_SPLITNAME_`. 2203 2204 `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields` 2205 2206 Developer Notes: 2207 This routine does not actually create the `IS` representing the split, that is delayed 2208 until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be 2209 available when this routine is called. 2210 2211 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`, 2212 `MatSetBlockSize()`, `MatCreateNest()` 2213 @*/ 2214 PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[]) 2215 { 2216 PetscFunctionBegin; 2217 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2218 PetscAssertPointer(splitname, 2); 2219 PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname); 2220 PetscAssertPointer(fields, 4); 2221 PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col)); 2222 PetscFunctionReturn(PETSC_SUCCESS); 2223 } 2224 2225 /*@ 2226 PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build 2227 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2228 2229 Logically Collective 2230 2231 Input Parameters: 2232 + pc - the preconditioner object 2233 - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from 2234 2235 Options Database Key: 2236 . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks 2237 2238 Level: intermediate 2239 2240 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT` 2241 @*/ 2242 PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg) 2243 { 2244 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2245 PetscBool isfs; 2246 2247 PetscFunctionBegin; 2248 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2249 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2250 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2251 jac->diag_use_amat = flg; 2252 PetscFunctionReturn(PETSC_SUCCESS); 2253 } 2254 2255 /*@ 2256 PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build 2257 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2258 2259 Logically Collective 2260 2261 Input Parameter: 2262 . pc - the preconditioner object 2263 2264 Output Parameter: 2265 . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from 2266 2267 Level: intermediate 2268 2269 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT` 2270 @*/ 2271 PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg) 2272 { 2273 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2274 PetscBool isfs; 2275 2276 PetscFunctionBegin; 2277 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2278 PetscAssertPointer(flg, 2); 2279 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2280 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2281 *flg = jac->diag_use_amat; 2282 PetscFunctionReturn(PETSC_SUCCESS); 2283 } 2284 2285 /*@ 2286 PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build 2287 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2288 2289 Logically Collective 2290 2291 Input Parameters: 2292 + pc - the preconditioner object 2293 - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from 2294 2295 Options Database Key: 2296 . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks 2297 2298 Level: intermediate 2299 2300 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT` 2301 @*/ 2302 PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg) 2303 { 2304 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2305 PetscBool isfs; 2306 2307 PetscFunctionBegin; 2308 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2309 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2310 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2311 jac->offdiag_use_amat = flg; 2312 PetscFunctionReturn(PETSC_SUCCESS); 2313 } 2314 2315 /*@ 2316 PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build 2317 the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators. 2318 2319 Logically Collective 2320 2321 Input Parameter: 2322 . pc - the preconditioner object 2323 2324 Output Parameter: 2325 . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from 2326 2327 Level: intermediate 2328 2329 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT` 2330 @*/ 2331 PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg) 2332 { 2333 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2334 PetscBool isfs; 2335 2336 PetscFunctionBegin; 2337 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2338 PetscAssertPointer(flg, 2); 2339 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 2340 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT); 2341 *flg = jac->offdiag_use_amat; 2342 PetscFunctionReturn(PETSC_SUCCESS); 2343 } 2344 2345 /*@ 2346 PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT` 2347 2348 Logically Collective 2349 2350 Input Parameters: 2351 + pc - the preconditioner context 2352 . splitname - name of this split, if `NULL` the number of the split is used 2353 - is - the index set that defines the elements in this split 2354 2355 Level: intermediate 2356 2357 Notes: 2358 Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST` 2359 2360 This function is called once per split (it creates a new split each time). Solve options 2361 for this split will be available under the prefix -fieldsplit_SPLITNAME_. 2362 2363 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()` 2364 @*/ 2365 PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is) 2366 { 2367 PetscFunctionBegin; 2368 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2369 if (splitname) PetscAssertPointer(splitname, 2); 2370 PetscValidHeaderSpecific(is, IS_CLASSID, 3); 2371 PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is)); 2372 PetscFunctionReturn(PETSC_SUCCESS); 2373 } 2374 2375 /*@ 2376 PCFieldSplitGetIS - Retrieves the elements for a split as an `IS` 2377 2378 Logically Collective 2379 2380 Input Parameters: 2381 + pc - the preconditioner context 2382 - splitname - name of this split 2383 2384 Output Parameter: 2385 . is - the index set that defines the elements in this split, or `NULL` if the split is not found 2386 2387 Level: intermediate 2388 2389 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()` 2390 @*/ 2391 PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is) 2392 { 2393 PetscFunctionBegin; 2394 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2395 PetscAssertPointer(splitname, 2); 2396 PetscAssertPointer(is, 3); 2397 { 2398 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2399 PC_FieldSplitLink ilink = jac->head; 2400 PetscBool found; 2401 2402 *is = NULL; 2403 while (ilink) { 2404 PetscCall(PetscStrcmp(ilink->splitname, splitname, &found)); 2405 if (found) { 2406 *is = ilink->is; 2407 break; 2408 } 2409 ilink = ilink->next; 2410 } 2411 } 2412 PetscFunctionReturn(PETSC_SUCCESS); 2413 } 2414 2415 /*@ 2416 PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS` 2417 2418 Logically Collective 2419 2420 Input Parameters: 2421 + pc - the preconditioner context 2422 - index - index of this split 2423 2424 Output Parameter: 2425 . is - the index set that defines the elements in this split 2426 2427 Level: intermediate 2428 2429 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`, 2430 2431 @*/ 2432 PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is) 2433 { 2434 PetscFunctionBegin; 2435 PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index); 2436 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2437 PetscAssertPointer(is, 3); 2438 { 2439 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2440 PC_FieldSplitLink ilink = jac->head; 2441 PetscInt i = 0; 2442 PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits); 2443 2444 while (i < index) { 2445 ilink = ilink->next; 2446 ++i; 2447 } 2448 PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is)); 2449 } 2450 PetscFunctionReturn(PETSC_SUCCESS); 2451 } 2452 2453 /*@ 2454 PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the 2455 fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used. 2456 2457 Logically Collective 2458 2459 Input Parameters: 2460 + pc - the preconditioner context 2461 - bs - the block size 2462 2463 Level: intermediate 2464 2465 Note: 2466 If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields. 2467 2468 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 2469 @*/ 2470 PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs) 2471 { 2472 PetscFunctionBegin; 2473 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2474 PetscValidLogicalCollectiveInt(pc, bs, 2); 2475 PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs)); 2476 PetscFunctionReturn(PETSC_SUCCESS); 2477 } 2478 2479 /*@C 2480 PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits 2481 2482 Collective 2483 2484 Input Parameter: 2485 . pc - the preconditioner context 2486 2487 Output Parameters: 2488 + n - the number of splits 2489 - subksp - the array of `KSP` contexts 2490 2491 Level: advanced 2492 2493 Notes: 2494 After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()` 2495 (not the `KSP`, just the array that contains them). 2496 2497 You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`. 2498 2499 If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the 2500 Schur complement and the `KSP` object used to iterate over the Schur complement. 2501 To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`. 2502 2503 If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the 2504 inner linear system defined by the matrix H in each loop. 2505 2506 Fortran Note: 2507 Call `PCFieldSplitRestoreSubKSP()` when the array of `KSP` is no longer needed 2508 2509 Developer Notes: 2510 There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()` 2511 2512 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()` 2513 @*/ 2514 PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[]) 2515 { 2516 PetscFunctionBegin; 2517 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2518 if (n) PetscAssertPointer(n, 2); 2519 PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp)); 2520 PetscFunctionReturn(PETSC_SUCCESS); 2521 } 2522 2523 /*@C 2524 PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT` 2525 2526 Collective 2527 2528 Input Parameter: 2529 . pc - the preconditioner context 2530 2531 Output Parameters: 2532 + n - the number of splits 2533 - subksp - the array of `KSP` contexts 2534 2535 Level: advanced 2536 2537 Notes: 2538 After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()` 2539 (not the `KSP` just the array that contains them). 2540 2541 You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`. 2542 2543 If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order) 2544 + 1 - the `KSP` used for the (1,1) block 2545 . 2 - the `KSP` used for the Schur complement (not the one used for the interior Schur solver) 2546 - 3 - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block). 2547 2548 It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`. 2549 2550 Fortran Note: 2551 Call `PCFieldSplitSchurRestoreSubKSP()` when the array of `KSP` is no longer needed 2552 2553 Developer Notes: 2554 There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()` 2555 2556 Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged? 2557 2558 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()` 2559 @*/ 2560 PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[]) 2561 { 2562 PetscFunctionBegin; 2563 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2564 if (n) PetscAssertPointer(n, 2); 2565 PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp)); 2566 PetscFunctionReturn(PETSC_SUCCESS); 2567 } 2568 2569 /*@ 2570 PCFieldSplitSetSchurPre - Indicates from what operator the preconditioner is constructed for the Schur complement. 2571 The default is the A11 matrix. 2572 2573 Collective 2574 2575 Input Parameters: 2576 + pc - the preconditioner context 2577 . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default), 2578 `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`, 2579 `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL` 2580 - pre - matrix to use for preconditioning, or `NULL` 2581 2582 Options Database Keys: 2583 + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments 2584 - -fieldsplit_1_pc_type <pctype> - the preconditioner algorithm that is used to construct the preconditioner from the operator 2585 2586 Level: intermediate 2587 2588 Notes: 2589 If ptype is 2590 + a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner 2591 matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix 2592 . self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix: 2593 The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM` 2594 . user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument 2595 to this function). 2596 . selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $ 2597 This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be 2598 lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump` 2599 - full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation 2600 computed internally by `PCFIELDSPLIT` (this is expensive) 2601 useful mostly as a test that the Schur complement approach can work for your problem 2602 2603 When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense 2604 with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and 2605 `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement. 2606 2607 Developer Note: 2608 The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere. 2609 2610 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, 2611 `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()` 2612 @*/ 2613 PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2614 { 2615 PetscFunctionBegin; 2616 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2617 PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre)); 2618 PetscFunctionReturn(PETSC_SUCCESS); 2619 } 2620 2621 PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2622 { 2623 return PCFieldSplitSetSchurPre(pc, ptype, pre); 2624 } /* Deprecated name */ 2625 2626 /*@ 2627 PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be 2628 preconditioned. See `PCFieldSplitSetSchurPre()` for details. 2629 2630 Logically Collective 2631 2632 Input Parameter: 2633 . pc - the preconditioner context 2634 2635 Output Parameters: 2636 + 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` 2637 - pre - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL` 2638 2639 Level: intermediate 2640 2641 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC` 2642 @*/ 2643 PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre) 2644 { 2645 PetscFunctionBegin; 2646 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2647 PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre)); 2648 PetscFunctionReturn(PETSC_SUCCESS); 2649 } 2650 2651 /*@ 2652 PCFieldSplitSchurGetS - extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately 2653 2654 Not Collective 2655 2656 Input Parameter: 2657 . pc - the preconditioner context 2658 2659 Output Parameter: 2660 . S - the Schur complement matrix 2661 2662 Level: advanced 2663 2664 Note: 2665 This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`. 2666 2667 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`, 2668 `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()` 2669 @*/ 2670 PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S) 2671 { 2672 const char *t; 2673 PetscBool isfs; 2674 PC_FieldSplit *jac; 2675 2676 PetscFunctionBegin; 2677 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2678 PetscCall(PetscObjectGetType((PetscObject)pc, &t)); 2679 PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs)); 2680 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t); 2681 jac = (PC_FieldSplit *)pc->data; 2682 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type); 2683 if (S) *S = jac->schur; 2684 PetscFunctionReturn(PETSC_SUCCESS); 2685 } 2686 2687 /*@ 2688 PCFieldSplitSchurRestoreS - returns the `MATSCHURCOMPLEMENT` matrix used by this `PC` 2689 2690 Not Collective 2691 2692 Input Parameters: 2693 + pc - the preconditioner context 2694 - S - the Schur complement matrix 2695 2696 Level: advanced 2697 2698 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()` 2699 @*/ 2700 PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S) 2701 { 2702 const char *t; 2703 PetscBool isfs; 2704 PC_FieldSplit *jac; 2705 2706 PetscFunctionBegin; 2707 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2708 PetscCall(PetscObjectGetType((PetscObject)pc, &t)); 2709 PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs)); 2710 PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t); 2711 jac = (PC_FieldSplit *)pc->data; 2712 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type); 2713 PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten"); 2714 PetscFunctionReturn(PETSC_SUCCESS); 2715 } 2716 2717 static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre) 2718 { 2719 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2720 2721 PetscFunctionBegin; 2722 jac->schurpre = ptype; 2723 if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) { 2724 PetscCall(MatDestroy(&jac->schur_user)); 2725 jac->schur_user = pre; 2726 PetscCall(PetscObjectReference((PetscObject)jac->schur_user)); 2727 } 2728 PetscFunctionReturn(PETSC_SUCCESS); 2729 } 2730 2731 static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre) 2732 { 2733 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2734 2735 PetscFunctionBegin; 2736 if (ptype) *ptype = jac->schurpre; 2737 if (pre) *pre = jac->schur_user; 2738 PetscFunctionReturn(PETSC_SUCCESS); 2739 } 2740 2741 /*@ 2742 PCFieldSplitSetSchurFactType - sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note` 2743 2744 Collective 2745 2746 Input Parameters: 2747 + pc - the preconditioner context 2748 - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default 2749 2750 Options Database Key: 2751 . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full` 2752 2753 Level: intermediate 2754 2755 Notes: 2756 The `full` factorization is 2757 2758 ```{math} 2759 \left(\begin{array}{cc} A & B \\ 2760 C & E \\ 2761 \end{array}\right) = 2762 \left(\begin{array}{cc} I & 0 \\ 2763 C A^{-1} & I \\ 2764 \end{array}\right) 2765 \left(\begin{array}{cc} A & 0 \\ 2766 0 & S \\ 2767 \end{array}\right) 2768 \left(\begin{array}{cc} I & A^{-1}B \\ 2769 0 & I \\ 2770 \end{array}\right) = L D U, 2771 ``` 2772 2773 where $ S = E - C A^{-1} B $. In practice, the full factorization is applied via block triangular solves with the grouping $L(DU)$. `upper` uses $DU$, `lower` uses $LD$, 2774 and `diag` is the diagonal part with the sign of $S$ flipped (because this makes the preconditioner positive definite for many formulations, 2775 thus allowing the use of `KSPMINRES)`. Sign flipping of $S$ can be turned off with `PCFieldSplitSetSchurScale()`. 2776 2777 If $A$ and $S$ are solved exactly 2778 + 1 - `full` factorization is a direct solver. 2779 . 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. 2780 - 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. 2781 2782 If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner 2783 application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice. 2784 2785 For symmetric problems in which $A$ is positive definite and $S$ is negative definite, `diag` can be used with `KSPMINRES`. 2786 2787 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 $S$). 2788 2789 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`, 2790 [](sec_flexibleksp), `PCFieldSplitSetSchurPre()` 2791 @*/ 2792 PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype) 2793 { 2794 PetscFunctionBegin; 2795 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2796 PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype)); 2797 PetscFunctionReturn(PETSC_SUCCESS); 2798 } 2799 2800 static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype) 2801 { 2802 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2803 2804 PetscFunctionBegin; 2805 jac->schurfactorization = ftype; 2806 PetscFunctionReturn(PETSC_SUCCESS); 2807 } 2808 2809 /*@ 2810 PCFieldSplitSetSchurScale - Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`. 2811 2812 Collective 2813 2814 Input Parameters: 2815 + pc - the preconditioner context 2816 - scale - scaling factor for the Schur complement 2817 2818 Options Database Key: 2819 . -pc_fieldsplit_schur_scale <scale> - default is -1.0 2820 2821 Level: intermediate 2822 2823 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()` 2824 @*/ 2825 PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale) 2826 { 2827 PetscFunctionBegin; 2828 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2829 PetscValidLogicalCollectiveScalar(pc, scale, 2); 2830 PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale)); 2831 PetscFunctionReturn(PETSC_SUCCESS); 2832 } 2833 2834 static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale) 2835 { 2836 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2837 2838 PetscFunctionBegin; 2839 jac->schurscale = scale; 2840 PetscFunctionReturn(PETSC_SUCCESS); 2841 } 2842 2843 /*@C 2844 PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement 2845 2846 Collective 2847 2848 Input Parameter: 2849 . pc - the preconditioner context 2850 2851 Output Parameters: 2852 + A00 - the (0,0) block 2853 . A01 - the (0,1) block 2854 . A10 - the (1,0) block 2855 - A11 - the (1,1) block 2856 2857 Level: advanced 2858 2859 Note: 2860 Use `NULL` for any unneeded output arguments 2861 2862 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()` 2863 @*/ 2864 PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11) 2865 { 2866 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2867 2868 PetscFunctionBegin; 2869 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2870 PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach."); 2871 if (A00) *A00 = jac->pmat[0]; 2872 if (A01) *A01 = jac->B; 2873 if (A10) *A10 = jac->C; 2874 if (A11) *A11 = jac->pmat[1]; 2875 PetscFunctionReturn(PETSC_SUCCESS); 2876 } 2877 2878 /*@ 2879 PCFieldSplitSetGKBTol - Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 2880 2881 Collective 2882 2883 Input Parameters: 2884 + pc - the preconditioner context 2885 - tolerance - the solver tolerance 2886 2887 Options Database Key: 2888 . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5 2889 2890 Level: intermediate 2891 2892 Note: 2893 The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion. 2894 It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than 2895 this estimate, the stopping criterion is satisfactory in practical cases. 2896 2897 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()` 2898 @*/ 2899 PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance) 2900 { 2901 PetscFunctionBegin; 2902 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2903 PetscValidLogicalCollectiveReal(pc, tolerance, 2); 2904 PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance)); 2905 PetscFunctionReturn(PETSC_SUCCESS); 2906 } 2907 2908 static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance) 2909 { 2910 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2911 2912 PetscFunctionBegin; 2913 jac->gkbtol = tolerance; 2914 PetscFunctionReturn(PETSC_SUCCESS); 2915 } 2916 2917 /*@ 2918 PCFieldSplitSetGKBMaxit - Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 2919 2920 Collective 2921 2922 Input Parameters: 2923 + pc - the preconditioner context 2924 - maxit - the maximum number of iterations 2925 2926 Options Database Key: 2927 . -pc_fieldsplit_gkb_maxit <maxit> - default is 100 2928 2929 Level: intermediate 2930 2931 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()` 2932 @*/ 2933 PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit) 2934 { 2935 PetscFunctionBegin; 2936 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2937 PetscValidLogicalCollectiveInt(pc, maxit, 2); 2938 PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit)); 2939 PetscFunctionReturn(PETSC_SUCCESS); 2940 } 2941 2942 static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit) 2943 { 2944 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2945 2946 PetscFunctionBegin; 2947 jac->gkbmaxit = maxit; 2948 PetscFunctionReturn(PETSC_SUCCESS); 2949 } 2950 2951 /*@ 2952 PCFieldSplitSetGKBDelay - Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT` 2953 preconditioner. 2954 2955 Collective 2956 2957 Input Parameters: 2958 + pc - the preconditioner context 2959 - delay - the delay window in the lower bound estimate 2960 2961 Options Database Key: 2962 . -pc_fieldsplit_gkb_delay <delay> - default is 5 2963 2964 Level: intermediate 2965 2966 Notes: 2967 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 $ 2968 is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs 2969 at least (`delay` + 1) iterations to stop. 2970 2971 For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013` 2972 2973 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()` 2974 @*/ 2975 PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay) 2976 { 2977 PetscFunctionBegin; 2978 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 2979 PetscValidLogicalCollectiveInt(pc, delay, 2); 2980 PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay)); 2981 PetscFunctionReturn(PETSC_SUCCESS); 2982 } 2983 2984 static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay) 2985 { 2986 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 2987 2988 PetscFunctionBegin; 2989 jac->gkbdelay = delay; 2990 PetscFunctionReturn(PETSC_SUCCESS); 2991 } 2992 2993 /*@ 2994 PCFieldSplitSetGKBNu - Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the 2995 Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT` 2996 2997 Collective 2998 2999 Input Parameters: 3000 + pc - the preconditioner context 3001 - nu - the shift parameter 3002 3003 Options Database Key: 3004 . -pc_fieldsplit_gkb_nu <nu> - default is 1 3005 3006 Level: intermediate 3007 3008 Notes: 3009 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, 3010 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 3011 necessary to find a good balance in between the convergence of the inner and outer loop. 3012 3013 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. 3014 3015 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()` 3016 @*/ 3017 PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu) 3018 { 3019 PetscFunctionBegin; 3020 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3021 PetscValidLogicalCollectiveReal(pc, nu, 2); 3022 PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu)); 3023 PetscFunctionReturn(PETSC_SUCCESS); 3024 } 3025 3026 static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu) 3027 { 3028 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3029 3030 PetscFunctionBegin; 3031 jac->gkbnu = nu; 3032 PetscFunctionReturn(PETSC_SUCCESS); 3033 } 3034 3035 static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type) 3036 { 3037 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3038 3039 PetscFunctionBegin; 3040 jac->type = type; 3041 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL)); 3042 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL)); 3043 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL)); 3044 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL)); 3045 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL)); 3046 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL)); 3047 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL)); 3048 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL)); 3049 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL)); 3050 3051 if (type == PC_COMPOSITE_SCHUR) { 3052 pc->ops->apply = PCApply_FieldSplit_Schur; 3053 pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur; 3054 pc->ops->view = PCView_FieldSplit_Schur; 3055 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit_Schur; 3056 3057 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur)); 3058 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit)); 3059 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit)); 3060 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit)); 3061 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit)); 3062 } else if (type == PC_COMPOSITE_GKB) { 3063 pc->ops->apply = PCApply_FieldSplit_GKB; 3064 pc->ops->applytranspose = NULL; 3065 pc->ops->view = PCView_FieldSplit_GKB; 3066 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit_GKB; 3067 3068 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit)); 3069 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit)); 3070 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit)); 3071 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit)); 3072 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit)); 3073 } else { 3074 pc->ops->apply = PCApply_FieldSplit; 3075 pc->ops->applytranspose = PCApplyTranspose_FieldSplit; 3076 pc->ops->view = PCView_FieldSplit; 3077 pc->ops->setuponblocks = PCSetUpOnBlocks_FieldSplit; 3078 3079 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit)); 3080 } 3081 PetscFunctionReturn(PETSC_SUCCESS); 3082 } 3083 3084 static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs) 3085 { 3086 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3087 3088 PetscFunctionBegin; 3089 PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs); 3090 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); 3091 jac->bs = bs; 3092 PetscFunctionReturn(PETSC_SUCCESS); 3093 } 3094 3095 static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[]) 3096 { 3097 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3098 PC_FieldSplitLink ilink_current = jac->head; 3099 IS is_owned; 3100 3101 PetscFunctionBegin; 3102 jac->coordinates_set = PETSC_TRUE; // Internal flag 3103 PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL)); 3104 3105 while (ilink_current) { 3106 // For each IS, embed it to get local coords indces 3107 IS is_coords; 3108 PetscInt ndofs_block; 3109 const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block 3110 3111 // Setting drop to true for safety. It should make no difference. 3112 PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords)); 3113 PetscCall(ISGetLocalSize(is_coords, &ndofs_block)); 3114 PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration)); 3115 3116 // Allocate coordinates vector and set it directly 3117 PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords)); 3118 for (PetscInt dof = 0; dof < ndofs_block; ++dof) { 3119 for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d]; 3120 } 3121 ilink_current->dim = dim; 3122 ilink_current->ndofs = ndofs_block; 3123 PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration)); 3124 PetscCall(ISDestroy(&is_coords)); 3125 ilink_current = ilink_current->next; 3126 } 3127 PetscCall(ISDestroy(&is_owned)); 3128 PetscFunctionReturn(PETSC_SUCCESS); 3129 } 3130 3131 /*@ 3132 PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT` 3133 3134 Collective 3135 3136 Input Parameters: 3137 + pc - the preconditioner context 3138 - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, 3139 `PC_COMPOSITE_GKB` 3140 3141 Options Database Key: 3142 . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type 3143 3144 Level: intermediate 3145 3146 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, 3147 `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()` 3148 @*/ 3149 PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type) 3150 { 3151 PetscFunctionBegin; 3152 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3153 PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type)); 3154 PetscFunctionReturn(PETSC_SUCCESS); 3155 } 3156 3157 /*@ 3158 PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT` 3159 3160 Not collective 3161 3162 Input Parameter: 3163 . pc - the preconditioner context 3164 3165 Output Parameter: 3166 . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR` 3167 3168 Level: intermediate 3169 3170 .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`, 3171 `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR` 3172 @*/ 3173 PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type) 3174 { 3175 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3176 3177 PetscFunctionBegin; 3178 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3179 PetscAssertPointer(type, 2); 3180 *type = jac->type; 3181 PetscFunctionReturn(PETSC_SUCCESS); 3182 } 3183 3184 /*@ 3185 PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible. 3186 3187 Logically Collective 3188 3189 Input Parameters: 3190 + pc - the preconditioner context 3191 - flg - boolean indicating whether to use field splits defined by the `DM` 3192 3193 Options Database Key: 3194 . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM` 3195 3196 Level: intermediate 3197 3198 Developer Note: 3199 The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database 3200 3201 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 3202 @*/ 3203 PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg) 3204 { 3205 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3206 PetscBool isfs; 3207 3208 PetscFunctionBegin; 3209 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3210 PetscValidLogicalCollectiveBool(pc, flg, 2); 3211 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 3212 if (isfs) jac->dm_splits = flg; 3213 PetscFunctionReturn(PETSC_SUCCESS); 3214 } 3215 3216 /*@ 3217 PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible. 3218 3219 Logically Collective 3220 3221 Input Parameter: 3222 . pc - the preconditioner context 3223 3224 Output Parameter: 3225 . flg - boolean indicating whether to use field splits defined by the `DM` 3226 3227 Level: intermediate 3228 3229 Developer Note: 3230 The name should be `PCFieldSplitGetUseDMSplits()` 3231 3232 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()` 3233 @*/ 3234 PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg) 3235 { 3236 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3237 PetscBool isfs; 3238 3239 PetscFunctionBegin; 3240 PetscValidHeaderSpecific(pc, PC_CLASSID, 1); 3241 PetscAssertPointer(flg, 2); 3242 PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs)); 3243 if (isfs) { 3244 if (flg) *flg = jac->dm_splits; 3245 } 3246 PetscFunctionReturn(PETSC_SUCCESS); 3247 } 3248 3249 /*@ 3250 PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries. 3251 3252 Logically Collective 3253 3254 Input Parameter: 3255 . pc - the preconditioner context 3256 3257 Output Parameter: 3258 . flg - boolean indicating whether to detect fields or not 3259 3260 Level: intermediate 3261 3262 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()` 3263 @*/ 3264 PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg) 3265 { 3266 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3267 3268 PetscFunctionBegin; 3269 *flg = jac->detect; 3270 PetscFunctionReturn(PETSC_SUCCESS); 3271 } 3272 3273 /*@ 3274 PCFieldSplitSetDetectSaddlePoint - Sets 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 Options Database Key: 3285 . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point 3286 3287 Level: intermediate 3288 3289 Note: 3290 Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`). 3291 3292 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF` 3293 @*/ 3294 PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg) 3295 { 3296 PC_FieldSplit *jac = (PC_FieldSplit *)pc->data; 3297 3298 PetscFunctionBegin; 3299 jac->detect = flg; 3300 if (jac->detect) { 3301 PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR)); 3302 PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL)); 3303 } 3304 PetscFunctionReturn(PETSC_SUCCESS); 3305 } 3306 3307 /*MC 3308 PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual 3309 collections of variables (that may overlap) called fields or splits. Each field often represents a different continuum variable 3310 represented on a grid, such as velocity, pressure, or temperature. 3311 In the literature these are sometimes called block preconditioners; but should not be confused with `PCBJACOBI`. 3312 See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details. 3313 3314 Options Database Keys: 3315 + -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split 3316 . -pc_fieldsplit_default - automatically add any fields to additional splits that have not 3317 been supplied explicitly by `-pc_fieldsplit_%d_fields` 3318 . -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields) 3319 when the matrix is not of `MatType` `MATNEST` 3320 . -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting 3321 . -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()` 3322 . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`; 3323 see `PCFieldSplitSetSchurFactType()` 3324 . -pc_fieldsplit_dm_splits <true,false> (default is true) - Whether to use `DMCreateFieldDecomposition()` for splits 3325 - -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver 3326 3327 Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` . 3328 The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_` 3329 For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields. 3330 3331 To set options on the solvers for all blocks, prepend `-fieldsplit_` to all the `PC` 3332 options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`. 3333 3334 To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()` 3335 and set the options directly on the resulting `KSP` object 3336 3337 Level: intermediate 3338 3339 Notes: 3340 Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()` 3341 to define a split by an arbitrary collection of entries. 3342 3343 If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports 3344 `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs, 3345 beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`, 3346 if this is not called the block size defaults to the blocksize of the second matrix passed 3347 to `KSPSetOperators()`/`PCSetOperators()`. 3348 3349 For the Schur complement preconditioner if 3350 ```{math} 3351 J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right] 3352 ``` 3353 3354 the preconditioner using `full` factorization is logically 3355 ```{math} 3356 \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{ksp}(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] 3357 ``` 3358 where the action of $\text{ksp}(A_{00})$ is applied using the `KSP` solver with prefix `-fieldsplit_0_`. $S$ is the Schur complement 3359 ```{math} 3360 S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01} 3361 ``` 3362 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` 3363 was given in providing the SECOND split or 1 if not given). Accordingly, if using `PCFieldSplitGetSubKSP()`, the array of sub-`KSP` contexts will hold two `KSP`s: at its 3364 0th index, the `KSP` associated with `-fieldsplit_0_`, and at its 1st index, the `KSP` corresponding to `-fieldsplit_1_`. 3365 By default, $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$. 3366 3367 The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above, 3368 `diag` gives 3369 ```{math} 3370 \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\ 0 & -\text{ksp}(S) \end{array}\right] 3371 ``` 3372 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 3373 can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of 3374 ```{math} 3375 \left[\begin{array}{cc} A_{00} & 0 \\ A_{10} & S \end{array}\right] 3376 ``` 3377 where the inverses of $A_{00}$ and $S$ are applied using `KSP`s. The upper factorization is the inverse of 3378 ```{math} 3379 \left[\begin{array}{cc} A_{00} & A_{01} \\ 0 & S \end{array}\right] 3380 ``` 3381 where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s. 3382 3383 If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS` 3384 is used automatically for a second submatrix. 3385 3386 The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1. 3387 Generally it should be used with the `MATAIJ` or `MATNEST` `MatType` 3388 3389 The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see, 3390 for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`. 3391 One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers". 3392 3393 See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`. 3394 3395 The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the 3396 residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables. 3397 3398 The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape 3399 ```{math} 3400 \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right] 3401 ``` 3402 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 $H = _{A00} + \nu*A_{01}*A_{01}'$. 3403 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_`. 3404 3405 Some `PCFIELDSPLIT` variants are called physics-based preconditioners, since the preconditioner takes into account the underlying physics of the 3406 problem. But this nomenclature is not well-defined. 3407 3408 Developer Note: 3409 The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their 3410 user API. 3411 3412 .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`, 3413 `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`, 3414 `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`, 3415 `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()` 3416 M*/ 3417 3418 PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc) 3419 { 3420 PC_FieldSplit *jac; 3421 3422 PetscFunctionBegin; 3423 PetscCall(PetscNew(&jac)); 3424 3425 jac->bs = -1; 3426 jac->type = PC_COMPOSITE_MULTIPLICATIVE; 3427 jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */ 3428 jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL; 3429 jac->schurscale = -1.0; 3430 jac->dm_splits = PETSC_TRUE; 3431 jac->gkbtol = 1e-5; 3432 jac->gkbdelay = 5; 3433 jac->gkbnu = 1; 3434 jac->gkbmaxit = 100; 3435 3436 pc->data = (void *)jac; 3437 3438 pc->ops->setup = PCSetUp_FieldSplit; 3439 pc->ops->reset = PCReset_FieldSplit; 3440 pc->ops->destroy = PCDestroy_FieldSplit; 3441 pc->ops->setfromoptions = PCSetFromOptions_FieldSplit; 3442 pc->ops->applyrichardson = NULL; 3443 3444 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit)); 3445 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit)); 3446 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit)); 3447 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit)); 3448 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit)); 3449 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit)); 3450 PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit)); 3451 3452 /* Initialize function pointers */ 3453 PetscCall(PCFieldSplitSetType(pc, jac->type)); 3454 PetscFunctionReturn(PETSC_SUCCESS); 3455 } 3456