1 #pragma once 2 3 /* SUBMANSEC = PC */ 4 5 /*S 6 PC - Abstract PETSc object that manages all preconditioners including direct solvers such as `PCLU` 7 8 Level: beginner 9 10 .seealso: [](doc_linsolve), [](sec_pc), `PCCreate()`, `PCSetType()`, `PCType` 11 S*/ 12 typedef struct _p_PC *PC; 13 14 /*J 15 PCType - String with the name of a PETSc preconditioner 16 17 Level: beginner 18 19 Note: 20 `PCRegister()` is used to register preconditioners that are then accessible via `PCSetType()` 21 22 .seealso: [](doc_linsolve), [](sec_pc), `PCSetType()`, `PC`, `PCCreate()`, `PCRegister()`, `PCSetFromOptions()`, `PCLU`, `PCJACOBI`, `PCBJACOBI` 23 J*/ 24 typedef const char *PCType; 25 #define PCNONE "none" 26 #define PCJACOBI "jacobi" 27 #define PCSOR "sor" 28 #define PCLU "lu" 29 #define PCQR "qr" 30 #define PCSHELL "shell" 31 #define PCAMGX "amgx" 32 #define PCBJACOBI "bjacobi" 33 #define PCMG "mg" 34 #define PCEISENSTAT "eisenstat" 35 #define PCILU "ilu" 36 #define PCICC "icc" 37 #define PCASM "asm" 38 #define PCGASM "gasm" 39 #define PCKSP "ksp" 40 #define PCBJKOKKOS "bjkokkos" 41 #define PCCOMPOSITE "composite" 42 #define PCREDUNDANT "redundant" 43 #define PCSPAI "spai" 44 #define PCNN "nn" 45 #define PCCHOLESKY "cholesky" 46 #define PCPBJACOBI "pbjacobi" 47 #define PCVPBJACOBI "vpbjacobi" 48 #define PCMAT "mat" 49 #define PCHYPRE "hypre" 50 #define PCPARMS "parms" 51 #define PCFIELDSPLIT "fieldsplit" 52 #define PCTFS "tfs" 53 #define PCML "ml" 54 #define PCGALERKIN "galerkin" 55 #define PCEXOTIC "exotic" 56 #define PCCP "cp" 57 #define PCBFBT "bfbt" 58 #define PCLSC "lsc" 59 #define PCPYTHON "python" 60 #define PCPFMG "pfmg" 61 #define PCSMG "smg" 62 #define PCSYSPFMG "syspfmg" 63 #define PCREDISTRIBUTE "redistribute" 64 #define PCSVD "svd" 65 #define PCGAMG "gamg" 66 #define PCCHOWILUVIENNACL "chowiluviennacl" 67 #define PCROWSCALINGVIENNACL "rowscalingviennacl" 68 #define PCSAVIENNACL "saviennacl" 69 #define PCBDDC "bddc" 70 #define PCKACZMARZ "kaczmarz" 71 #define PCTELESCOPE "telescope" 72 #define PCPATCH "patch" 73 #define PCLMVM "lmvm" 74 #define PCHMG "hmg" 75 #define PCDEFLATION "deflation" 76 #define PCHPDDM "hpddm" 77 #define PCH2OPUS "h2opus" 78 #define PCMPI "mpi" 79 80 /*E 81 PCSide - If the preconditioner is to be applied to the left, right 82 or symmetrically around the operator. 83 84 Values: 85 + `PC_LEFT` - applied after the operator is applied 86 . `PC_RIGHT` - applied before the operator is applied 87 - `PC_SYMMETRIC` - a portion of the preconditioner is applied before the operator and the transpose of this portion is applied after the operator is applied. 88 89 Level: beginner 90 91 Note: 92 Certain `KSPType` support only a subset of `PCSide` values 93 94 .seealso: [](sec_pc), `PC`, `KSPSetPCSide()`, `KSP`, `KSPType` 95 E*/ 96 typedef enum { 97 PC_SIDE_DEFAULT = -1, 98 PC_LEFT, 99 PC_RIGHT, 100 PC_SYMMETRIC 101 } PCSide; 102 #define PC_SIDE_MAX (PC_SYMMETRIC + 1) 103 104 /*E 105 PCRichardsonConvergedReason - reason a `PCApplyRichardson()` method terminated 106 107 Level: advanced 108 109 .seealso: [](sec_pc), `KSPRICHARDSON`, `PC`, `PCApplyRichardson()` 110 E*/ 111 typedef enum { 112 PCRICHARDSON_CONVERGED_RTOL = 2, 113 PCRICHARDSON_CONVERGED_ATOL = 3, 114 PCRICHARDSON_CONVERGED_ITS = 4, 115 PCRICHARDSON_DIVERGED_DTOL = -4 116 } PCRichardsonConvergedReason; 117 118 /*E 119 PCJacobiType - What elements of the matrix are used to form the Jacobi preconditioner 120 121 Values: 122 + `PC_JACOBI_DIAGONAL` - use the diagonal entry, if it is zero use one 123 . `PC_JACOBI_ROWL1` - add sum of absolute values in row i, j != i, to diag_ii 124 . `PC_JACOBI_ROWMAX` - use the maximum absolute value in the row 125 - `PC_JACOBI_ROWSUM` - use the sum of the values in the row (not the absolute values) 126 127 Level: intermediate 128 129 .seealso: [](sec_pc), `PCJACOBI`, `PC` 130 E*/ 131 typedef enum { 132 PC_JACOBI_DIAGONAL, 133 PC_JACOBI_ROWL1, 134 PC_JACOBI_ROWMAX, 135 PC_JACOBI_ROWSUM 136 } PCJacobiType; 137 138 /*E 139 PCASMType - Type of additive Schwarz method to use 140 141 Values: 142 + `PC_ASM_BASIC` - Symmetric version where residuals from the ghost points are used 143 and computed values in ghost regions are added together. 144 Classical standard additive Schwarz as introduced in {cite}`dryja1987additive`. 145 . `PC_ASM_RESTRICT` - Residuals from ghost points are used but computed values in ghost 146 region are discarded {cite}`cs99`. Default. 147 . `PC_ASM_INTERPOLATE` - Residuals from ghost points are not used, computed values in ghost 148 region are added back in. 149 - `PC_ASM_NONE` - Residuals from ghost points are not used, computed ghost values are 150 discarded. Not very good. 151 152 Level: beginner 153 154 .seealso: [](sec_pc), `PC`, `PCASM`, `PCASMSetType()`, `PCGASMType` 155 E*/ 156 typedef enum { 157 PC_ASM_BASIC = 3, 158 PC_ASM_RESTRICT = 1, 159 PC_ASM_INTERPOLATE = 2, 160 PC_ASM_NONE = 0 161 } PCASMType; 162 163 /*E 164 PCGASMType - Type of generalized additive Schwarz method to use (differs from `PCASM` in allowing multiple processors per subdomain). 165 166 Values: 167 + `PC_GASM_BASIC` - Symmetric version where the full from the outer subdomain is used, and the resulting correction is applied 168 over the outer subdomains. As a result, points in the overlap will receive the sum of the corrections 169 from neighboring subdomains. Classical standard additive Schwarz {cite}`dryja1987additive`. 170 . `PC_GASM_RESTRICT` - Residual from the outer subdomain is used but the correction is restricted to the inner subdomain only 171 (i.e., zeroed out over the overlap portion of the outer subdomain before being applied). As a result, 172 each point will receive a correction only from the unique inner subdomain containing it (nonoverlapping covering 173 assumption) {cite}`cs99`. Default. 174 . `PC_GASM_INTERPOLATE` - Residual is zeroed out over the overlap portion of the outer subdomain, but the resulting correction is 175 applied over the outer subdomain. As a result, points in the overlap will receive the sum of the corrections 176 from neighboring subdomains. 177 - `PC_GASM_NONE` - Residuals and corrections are zeroed out outside the local subdomains. Not very good. 178 179 Level: beginner 180 181 Note: 182 Each subdomain has nested inner and outer parts. The inner subdomains are assumed to form a non-overlapping covering of the computational 183 domain, while the outer subdomains contain the inner subdomains and overlap with each other. This preconditioner will compute 184 a subdomain correction over each *outer* subdomain from a residual computed there, but its different variants will differ in 185 (a) how the outer subdomain residual is computed, and (b) how the outer subdomain correction is computed. 186 187 Developer Note: 188 Perhaps better to remove this since it matches `PCASMType` 189 190 .seealso: [](sec_pc), `PCGASM`, `PCASM`, `PC`, `PCGASMSetType()`, `PCASMType` 191 E*/ 192 typedef enum { 193 PC_GASM_BASIC = 3, 194 PC_GASM_RESTRICT = 1, 195 PC_GASM_INTERPOLATE = 2, 196 PC_GASM_NONE = 0 197 } PCGASMType; 198 199 /*E 200 PCCompositeType - Determines how two or more preconditioner are composed with the `PCType` of `PCCOMPOSITE` 201 202 Values: 203 + `PC_COMPOSITE_ADDITIVE` - results from application of all preconditioners are added together 204 . `PC_COMPOSITE_MULTIPLICATIVE` - preconditioners are applied sequentially to the residual freshly 205 computed after the previous preconditioner application 206 . `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE` - preconditioners are applied sequentially to the residual freshly 207 computed from first preconditioner to last and then back (Use only for symmetric matrices and preconditioners) 208 . `PC_COMPOSITE_SPECIAL` - This is very special for a matrix of the form $ \alpha I + R + S$ 209 where the first preconditioner is built from $\alpha I + S$ and second from $\alpha I + R$ 210 . `PC_COMPOSITE_SCHUR` - composes the Schur complement of the matrix from two blocks, see `PCFIELDSPLIT` 211 - `PC_COMPOSITE_GKB` - the generalized Golub-Kahan bidiagonalization preconditioner, see `PCFIELDSPLIT` 212 213 Level: beginner 214 215 .seealso: [](sec_pc), `PCCOMPOSITE`, `PCFIELDSPLIT`, `PC`, `PCCompositeSetType()`, `SNESCompositeType`, `PCCompositeSpecialSetAlpha()` 216 E*/ 217 typedef enum { 218 PC_COMPOSITE_ADDITIVE, 219 PC_COMPOSITE_MULTIPLICATIVE, 220 PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE, 221 PC_COMPOSITE_SPECIAL, 222 PC_COMPOSITE_SCHUR, 223 PC_COMPOSITE_GKB 224 } PCCompositeType; 225 226 /*E 227 PCFieldSplitSchurPreType - Determines how to precondition a Schur complement 228 229 Values: 230 + `PC_FIELDSPLIT_SCHUR_PRE_SELF` - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix. 231 The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM` 232 . `PC_FIELDSPLIT_SCHUR_PRE_SELFP` - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $Sp = A11 - A10 diag(A00)^{-1} A01$. 233 This is only a good preconditioner when $diag(A00)$ is a good preconditioner for $A00$. Optionally, $A00$ can be 234 lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump` 235 . `PC_FIELDSPLIT_SCHUR_PRE_A11` - the preconditioner for the Schur complement is generated from $A11$, not the Schur complement matrix 236 . `PC_FIELDSPLIT_SCHUR_PRE_USER` - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument 237 to this function). 238 - `PC_FIELDSPLIT_SCHUR_PRE_FULL` - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation 239 computed internally by `PCFIELDSPLIT` (this is expensive) useful mostly as a test that the Schur complement approach can work for your problem 240 241 Level: intermediate 242 243 .seealso: [](sec_pc), `PCFIELDSPLIT`, `PCFieldSplitSetSchurPre()`, `PC` 244 E*/ 245 typedef enum { 246 PC_FIELDSPLIT_SCHUR_PRE_SELF, 247 PC_FIELDSPLIT_SCHUR_PRE_SELFP, 248 PC_FIELDSPLIT_SCHUR_PRE_A11, 249 PC_FIELDSPLIT_SCHUR_PRE_USER, 250 PC_FIELDSPLIT_SCHUR_PRE_FULL 251 } PCFieldSplitSchurPreType; 252 253 /*E 254 PCFieldSplitSchurFactType - determines which off-diagonal parts of the approximate block factorization to use 255 256 Values: 257 + `PC_FIELDSPLIT_SCHUR_FACT_DIAG` - the preconditioner is solving `D` 258 . `PC_FIELDSPLIT_SCHUR_FACT_LOWER` - the preconditioner is solving `L D` 259 . `PC_FIELDSPLIT_SCHUR_FACT_UPPER` - the preconditioner is solving `D U` 260 - `PC_FIELDSPLIT_SCHUR_FACT_FULL` - the preconditioner is solving `L(D U)` 261 262 where the matrix is factorized as 263 .vb 264 (A B) = (1 0) (A 0) (1 Ainv*B) = L D U 265 (C E) (C*Ainv 1) (0 S) (0 1) 266 .ve 267 268 Level: intermediate 269 270 .seealso: [](sec_pc), `PCFIELDSPLIT`, `PCFieldSplitSetSchurFactType()`, `PC` 271 E*/ 272 typedef enum { 273 PC_FIELDSPLIT_SCHUR_FACT_DIAG, 274 PC_FIELDSPLIT_SCHUR_FACT_LOWER, 275 PC_FIELDSPLIT_SCHUR_FACT_UPPER, 276 PC_FIELDSPLIT_SCHUR_FACT_FULL 277 } PCFieldSplitSchurFactType; 278 279 /*E 280 PCPARMSGlobalType - Determines the global preconditioner method in `PCPARMS` 281 282 Level: intermediate 283 284 .seealso: [](sec_pc), `PCPARMS`, `PCPARMSSetGlobal()`, `PC` 285 E*/ 286 typedef enum { 287 PC_PARMS_GLOBAL_RAS, 288 PC_PARMS_GLOBAL_SCHUR, 289 PC_PARMS_GLOBAL_BJ 290 } PCPARMSGlobalType; 291 292 /*E 293 PCPARMSLocalType - Determines the local preconditioner method in `PCPARMS` 294 295 Level: intermediate 296 297 .seealso: [](sec_pc), `PCPARMS`, `PCPARMSSetLocal()`, `PC` 298 E*/ 299 typedef enum { 300 PC_PARMS_LOCAL_ILU0, 301 PC_PARMS_LOCAL_ILUK, 302 PC_PARMS_LOCAL_ILUT, 303 PC_PARMS_LOCAL_ARMS 304 } PCPARMSLocalType; 305 306 /*J 307 PCGAMGType - type of generalized algebraic multigrid `PCGAMG` method 308 309 Values: 310 + `PCGAMGAGG` - (the default) smoothed aggregation algorithm, robust, very well tested 311 . `PCGAMGGEO` - geometric coarsening, uses mesh generator to produce coarser meshes, limited to triangles, not supported, reference implementation (2D) 312 - `PCGAMGCLASSICAL` - classical algebraic multigrid preconditioner, incomplete, not supported, reference implementation 313 314 Level: intermediate 315 316 .seealso: [](sec_pc), `PCGAMG`, `PCMG`, `PC`, `PCSetType()`, `PCGAMGSetThreshold()`, `PCGAMGSetThreshold()`, `PCGAMGSetReuseInterpolation()` 317 J*/ 318 typedef const char *PCGAMGType; 319 #define PCGAMGAGG "agg" 320 #define PCGAMGGEO "geo" 321 #define PCGAMGCLASSICAL "classical" 322 323 typedef const char *PCGAMGClassicalType; 324 #define PCGAMGCLASSICALDIRECT "direct" 325 #define PCGAMGCLASSICALSTANDARD "standard" 326 327 /*E 328 PCMGType - Determines the type of multigrid method that is run. 329 330 Values: 331 + `PC_MG_MULTIPLICATIVE` (default) - traditional V or W cycle as determined by `PCMGSetCycleType()` 332 . `PC_MG_ADDITIVE` - the additive multigrid preconditioner where all levels are 333 smoothed before updating the residual. This only uses the 334 down smoother, in the preconditioner the upper smoother is ignored 335 . `PC_MG_FULL` - same as multiplicative except one also performs grid sequencing, 336 that is starts on the coarsest grid, performs a cycle, interpolates 337 to the next, performs a cycle etc. This is much like the F-cycle presented in "Multigrid" by Trottenberg, Oosterlee, Schuller page 49, but that 338 algorithm supports smoothing on before the restriction on each level in the initial restriction to the coarsest stage. In addition that algorithm 339 calls the V-cycle only on the coarser level and has a post-smoother instead. 340 - `PC_MG_KASKADE` - like full multigrid except one never goes back to a coarser level from a finer 341 342 Level: beginner 343 344 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetType()`, `PCMGSetCycleType()`, `PCMGSetCycleTypeOnLevel()` 345 E*/ 346 typedef enum { 347 PC_MG_MULTIPLICATIVE, 348 PC_MG_ADDITIVE, 349 PC_MG_FULL, 350 PC_MG_KASKADE 351 } PCMGType; 352 #define PC_MG_CASCADE PC_MG_KASKADE; 353 354 /*E 355 PCMGCycleType - Use V-cycle or W-cycle 356 357 Values: 358 + `PC_MG_V_CYCLE` - use the V cycle 359 - `PC_MG_W_CYCLE` - use the W cycle 360 361 Level: beginner 362 363 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetCycleType()` 364 E*/ 365 typedef enum { 366 PC_MG_CYCLE_V = 1, 367 PC_MG_CYCLE_W = 2 368 } PCMGCycleType; 369 370 /*E 371 PCMGalerkinType - Determines if the coarse grid operators are computed via the Galerkin process 372 373 Values: 374 + `PC_MG_GALERKIN_PMAT` - computes the pmat (matrix from which the preconditioner is built) via the Galerkin process from the finest grid 375 . `PC_MG_GALERKIN_MAT` - computes the mat (matrix used to apply the operator) via the Galerkin process from the finest grid 376 . `PC_MG_GALERKIN_BOTH` - computes both the mat and pmat via the Galerkin process (if pmat == mat the construction is only done once 377 - `PC_MG_GALERKIN_NONE` - neither operator is computed via the Galerkin process, the user must provide the operator 378 379 Level: beginner 380 381 Note: 382 Users should never set `PC_MG_GALERKIN_EXTERNAL`, it is used by `PCHYPRE` and `PCML` 383 384 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetCycleType()` 385 E*/ 386 typedef enum { 387 PC_MG_GALERKIN_BOTH, 388 PC_MG_GALERKIN_PMAT, 389 PC_MG_GALERKIN_MAT, 390 PC_MG_GALERKIN_NONE, 391 PC_MG_GALERKIN_EXTERNAL 392 } PCMGGalerkinType; 393 394 /*E 395 PCExoticType - Face based or wirebasket based coarse grid space 396 397 Level: beginner 398 399 .seealso: [](sec_pc), `PCExoticSetType()`, `PCEXOTIC` 400 E*/ 401 typedef enum { 402 PC_EXOTIC_FACE, 403 PC_EXOTIC_WIREBASKET 404 } PCExoticType; 405 406 /*E 407 PCBDDCInterfaceExtType - Defines how interface balancing is extended into the interior of subdomains. 408 409 Values: 410 + `PC_BDDC_INTERFACE_EXT_DIRICHLET` - solves Dirichlet interior problem; this is the standard BDDC algorithm 411 - `PC_BDDC_INTERFACE_EXT_LUMP` - skips interior solve; sometimes called M_1 and associated with "lumped FETI-DP" 412 413 Level: intermediate 414 415 .seealso: [](sec_pc), `PCBDDC`, `PC` 416 E*/ 417 typedef enum { 418 PC_BDDC_INTERFACE_EXT_DIRICHLET, 419 PC_BDDC_INTERFACE_EXT_LUMP 420 } PCBDDCInterfaceExtType; 421 422 /*E 423 PCMGCoarseSpaceType - Function space for coarse space for adaptive interpolation 424 425 Level: beginner 426 427 .seealso: [](sec_pc), `PCMGSetAdaptCoarseSpaceType()`, `PCMG`, `PC` 428 E*/ 429 typedef enum { 430 PCMG_ADAPT_NONE, 431 PCMG_ADAPT_POLYNOMIAL, 432 PCMG_ADAPT_HARMONIC, 433 PCMG_ADAPT_EIGENVECTOR, 434 PCMG_ADAPT_GENERALIZED_EIGENVECTOR, 435 PCMG_ADAPT_GDSW 436 } PCMGCoarseSpaceType; 437 438 /*E 439 PCPatchConstructType - The algorithm used to construct patches for the `PCPATCH` preconditioner 440 441 Level: beginner 442 443 .seealso: [](sec_pc), `PCPatchSetConstructType()`, `PCPATCH`, `PC` 444 E*/ 445 typedef enum { 446 PC_PATCH_STAR, 447 PC_PATCH_VANKA, 448 PC_PATCH_PARDECOMP, 449 PC_PATCH_USER, 450 PC_PATCH_PYTHON 451 } PCPatchConstructType; 452 453 /*E 454 PCDeflationSpaceType - Type of deflation 455 456 Values: 457 + `PC_DEFLATION_SPACE_HAAR` - directly assembled based on Haar (db2) wavelet with overflowed filter cuted-off 458 . `PC_DEFLATION_SPACE_DB2` - `MATCOMPOSITE` of 1-lvl matices based on db2 (2 coefficient Daubechies / Haar wavelet) 459 . `PC_DEFLATION_SPACE_DB4` - same as above, but with db4 (4 coefficient Daubechies) 460 . `PC_DEFLATION_SPACE_DB8` - same as above, but with db8 (8 coefficient Daubechies) 461 . `PC_DEFLATION_SPACE_DB16` - same as above, but with db16 (16 coefficient Daubechies) 462 . `PC_DEFLATION_SPACE_BIORTH22` - same as above, but with biorthogonal 2.2 (6 coefficients) 463 . `PC_DEFLATION_SPACE_MEYER` - same as above, but with Meyer/FIR (62 coefficients) 464 . `PC_DEFLATION_SPACE_AGGREGATION` - aggregates local indices (given by operator matrix distribution) into a subdomain 465 - `PC_DEFLATION_SPACE_USER` - indicates space set by user 466 467 Level: intermediate 468 469 Note: 470 Wavelet-based space (except Haar) can be used in multilevel deflation. 471 472 .seealso: [](sec_pc), `PCDeflationSetSpaceToCompute()`, `PCDEFLATION`, `PC` 473 E*/ 474 typedef enum { 475 PC_DEFLATION_SPACE_HAAR, 476 PC_DEFLATION_SPACE_DB2, 477 PC_DEFLATION_SPACE_DB4, 478 PC_DEFLATION_SPACE_DB8, 479 PC_DEFLATION_SPACE_DB16, 480 PC_DEFLATION_SPACE_BIORTH22, 481 PC_DEFLATION_SPACE_MEYER, 482 PC_DEFLATION_SPACE_AGGREGATION, 483 PC_DEFLATION_SPACE_USER 484 } PCDeflationSpaceType; 485 486 /*E 487 PCHPDDMCoarseCorrectionType - Type of coarse correction used by `PCHPDDM` 488 489 Values: 490 + `PC_HPDDM_COARSE_CORRECTION_DEFLATED` (default) - eq. (1) in `PCHPDDMShellApply()` 491 . `PC_HPDDM_COARSE_CORRECTION_ADDITIVE` - eq. (2) 492 . `PC_HPDDM_COARSE_CORRECTION_BALANCED` - eq. (3) 493 - `PC_HPDDM_COARSE_CORRECTION_NONE` - no coarse correction (mostly useful for debugging) 494 495 Level: intermediate 496 497 .seealso: [](sec_pc), `PCHPDDM`, `PC`, `PCSetType()`, `PCHPDDMShellApply()` 498 E*/ 499 typedef enum { 500 PC_HPDDM_COARSE_CORRECTION_DEFLATED, 501 PC_HPDDM_COARSE_CORRECTION_ADDITIVE, 502 PC_HPDDM_COARSE_CORRECTION_BALANCED, 503 PC_HPDDM_COARSE_CORRECTION_NONE 504 } PCHPDDMCoarseCorrectionType; 505 506 /*E 507 PCHPDDMSchurPreType - Type of `PCHPDDM` preconditioner for a `MATSCHURCOMPLEMENT` generated by `PCFIELDSPLIT` with `PCFieldSplitSchurPreType` set to `PC_FIELDSPLIT_SCHUR_PRE_SELF` 508 509 Values: 510 + `PC_HPDDM_SCHUR_PRE_LEAST_SQUARES` (default) - only with a near-zero A11 block and A10 = A01^T; a preconditioner for solving A01^T A00^-1 A01 x = b is built by approximating the Schur complement with (inv(sqrt(diag(A00))) A01)^T (inv(sqrt(diag(A00))) A01) and by considering the associated linear least squares problem 511 - `PC_HPDDM_SCHUR_PRE_GENEO` - only with A10 = A01^T, `PCHPDDMSetAuxiliaryMat()` called on the `PC` of the A00 block, and if A11 is nonzero, then `PCHPDDMSetAuxiliaryMat()` must be called on the associated `PC` as well (it is built automatically for the user otherwise); the Schur complement `PC` is set internally to `PCKSP`, with the prefix `-fieldsplit_1_pc_hpddm_`; the operator associated to the `PC` is spectrally equivalent to the original Schur complement 512 513 Level: advanced 514 515 .seealso: [](sec_pc), `PCHPDDM`, `PC`, `PCFIELDSPLIT`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PCFieldSplitSetSchurPre()`, `PCHPDDMSetAuxiliaryMat()` 516 E*/ 517 typedef enum { 518 PC_HPDDM_SCHUR_PRE_LEAST_SQUARES, 519 PC_HPDDM_SCHUR_PRE_GENEO, 520 } PCHPDDMSchurPreType; 521 522 /*E 523 PCFailedReason - indicates type of `PC` failure 524 525 Level: beginner 526 527 .seealso: [](sec_pc), `PC` 528 E*/ 529 typedef enum { 530 PC_SETUP_ERROR = -1, 531 PC_NOERROR, 532 PC_FACTOR_STRUCT_ZEROPIVOT, 533 PC_FACTOR_NUMERIC_ZEROPIVOT, 534 PC_FACTOR_OUTMEMORY, 535 PC_FACTOR_OTHER, 536 PC_INCONSISTENT_RHS, 537 PC_SUBPC_ERROR 538 } PCFailedReason; 539 540 /*E 541 PCGAMGLayoutType - Layout for reduced grids 542 543 Level: intermediate 544 545 .seealso: [](sec_pc), `PCGAMG`, `PC`, `PCGAMGSetCoarseGridLayoutType()` 546 E*/ 547 typedef enum { 548 PCGAMG_LAYOUT_COMPACT, 549 PCGAMG_LAYOUT_SPREAD 550 } PCGAMGLayoutType; 551