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 `PCRICHARDSON` `PCApplyRichardson()` method terminated 106 107 Level: advanced 108 109 .seealso: [](sec_pc), `PCRICHARDSON`, `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 inv(diag(A00)) 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 the block diagonal part of the matrix used to define the preconditioner, 236 associated with the Schur complement (i.e. A11), not the Schur complement matrix 237 . `PC_FIELDSPLIT_SCHUR_PRE_USER` - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument 238 to this function). 239 - `PC_FIELDSPLIT_SCHUR_PRE_FULL` - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation 240 computed internally by `PCFIELDSPLIT` (this is expensive) useful mostly as a test that the Schur complement approach can work for your problem 241 242 Level: intermediate 243 244 .seealso: [](sec_pc), `PCFIELDSPLIT`, `PCFieldSplitSetSchurPre()`, `PC` 245 E*/ 246 typedef enum { 247 PC_FIELDSPLIT_SCHUR_PRE_SELF, 248 PC_FIELDSPLIT_SCHUR_PRE_SELFP, 249 PC_FIELDSPLIT_SCHUR_PRE_A11, 250 PC_FIELDSPLIT_SCHUR_PRE_USER, 251 PC_FIELDSPLIT_SCHUR_PRE_FULL 252 } PCFieldSplitSchurPreType; 253 254 /*E 255 PCFieldSplitSchurFactType - determines which off-diagonal parts of the approximate block factorization to use 256 257 Values: 258 + `PC_FIELDSPLIT_SCHUR_FACT_DIAG` - the preconditioner is solving `D` 259 . `PC_FIELDSPLIT_SCHUR_FACT_LOWER` - the preconditioner is solving `L D` 260 . `PC_FIELDSPLIT_SCHUR_FACT_UPPER` - the preconditioner is solving `D U` 261 - `PC_FIELDSPLIT_SCHUR_FACT_FULL` - the preconditioner is solving `L(D U)` 262 263 where the matrix is factorized as 264 .vb 265 (A B) = (1 0) (A 0) (1 Ainv*B) = L D U 266 (C E) (C*Ainv 1) (0 S) (0 1) 267 .ve 268 269 Level: intermediate 270 271 .seealso: [](sec_pc), `PCFIELDSPLIT`, `PCFieldSplitSetSchurFactType()`, `PC` 272 E*/ 273 typedef enum { 274 PC_FIELDSPLIT_SCHUR_FACT_DIAG, 275 PC_FIELDSPLIT_SCHUR_FACT_LOWER, 276 PC_FIELDSPLIT_SCHUR_FACT_UPPER, 277 PC_FIELDSPLIT_SCHUR_FACT_FULL 278 } PCFieldSplitSchurFactType; 279 280 /*E 281 PCPARMSGlobalType - Determines the global preconditioner method in `PCPARMS` 282 283 Level: intermediate 284 285 .seealso: [](sec_pc), `PCPARMS`, `PCPARMSSetGlobal()`, `PC` 286 E*/ 287 typedef enum { 288 PC_PARMS_GLOBAL_RAS, 289 PC_PARMS_GLOBAL_SCHUR, 290 PC_PARMS_GLOBAL_BJ 291 } PCPARMSGlobalType; 292 293 /*E 294 PCPARMSLocalType - Determines the local preconditioner method in `PCPARMS` 295 296 Level: intermediate 297 298 .seealso: [](sec_pc), `PCPARMS`, `PCPARMSSetLocal()`, `PC` 299 E*/ 300 typedef enum { 301 PC_PARMS_LOCAL_ILU0, 302 PC_PARMS_LOCAL_ILUK, 303 PC_PARMS_LOCAL_ILUT, 304 PC_PARMS_LOCAL_ARMS 305 } PCPARMSLocalType; 306 307 /*J 308 PCGAMGType - type of generalized algebraic multigrid `PCGAMG` method 309 310 Values: 311 + `PCGAMGAGG` - (the default) smoothed aggregation algorithm, robust, very well tested 312 . `PCGAMGGEO` - geometric coarsening, uses mesh generator to produce coarser meshes, limited to triangles, not supported, reference implementation (2D) 313 - `PCGAMGCLASSICAL` - classical algebraic multigrid preconditioner, incomplete, not supported, reference implementation 314 315 Level: intermediate 316 317 .seealso: [](sec_pc), `PCGAMG`, `PCMG`, `PC`, `PCSetType()`, `PCGAMGSetThreshold()`, `PCGAMGSetThreshold()`, `PCGAMGSetReuseInterpolation()` 318 J*/ 319 typedef const char *PCGAMGType; 320 #define PCGAMGAGG "agg" 321 #define PCGAMGGEO "geo" 322 #define PCGAMGCLASSICAL "classical" 323 324 typedef const char *PCGAMGClassicalType; 325 #define PCGAMGCLASSICALDIRECT "direct" 326 #define PCGAMGCLASSICALSTANDARD "standard" 327 328 /*E 329 PCMGType - Determines the type of multigrid method that is run. 330 331 Values: 332 + `PC_MG_MULTIPLICATIVE` (default) - traditional V or W cycle as determined by `PCMGSetCycleType()` 333 . `PC_MG_ADDITIVE` - the additive multigrid preconditioner where all levels are 334 smoothed before updating the residual. This only uses the 335 down smoother, in the preconditioner the upper smoother is ignored 336 . `PC_MG_FULL` - same as multiplicative except one also performs grid sequencing, 337 that is starts on the coarsest grid, performs a cycle, interpolates 338 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 339 algorithm supports smoothing on before the restriction on each level in the initial restriction to the coarsest stage. In addition that algorithm 340 calls the V-cycle only on the coarser level and has a post-smoother instead. 341 - `PC_MG_KASKADE` - like full multigrid except one never goes back to a coarser level from a finer 342 343 Level: beginner 344 345 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetType()`, `PCMGSetCycleType()`, `PCMGSetCycleTypeOnLevel()` 346 E*/ 347 typedef enum { 348 PC_MG_MULTIPLICATIVE, 349 PC_MG_ADDITIVE, 350 PC_MG_FULL, 351 PC_MG_KASKADE 352 } PCMGType; 353 #define PC_MG_CASCADE PC_MG_KASKADE; 354 355 /*E 356 PCMGCycleType - Use V-cycle or W-cycle 357 358 Values: 359 + `PC_MG_V_CYCLE` - use the V cycle 360 - `PC_MG_W_CYCLE` - use the W cycle 361 362 Level: beginner 363 364 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetCycleType()` 365 E*/ 366 typedef enum { 367 PC_MG_CYCLE_V = 1, 368 PC_MG_CYCLE_W = 2 369 } PCMGCycleType; 370 371 /*E 372 PCMGalerkinType - Determines if the coarse grid operators are computed via the Galerkin process 373 374 Values: 375 + `PC_MG_GALERKIN_PMAT` - computes the pmat (matrix from which the preconditioner is built) via the Galerkin process from the finest grid 376 . `PC_MG_GALERKIN_MAT` - computes the mat (matrix used to apply the operator) via the Galerkin process from the finest grid 377 . `PC_MG_GALERKIN_BOTH` - computes both the mat and pmat via the Galerkin process (if pmat == mat the construction is only done once 378 - `PC_MG_GALERKIN_NONE` - neither operator is computed via the Galerkin process, the user must provide the operator 379 380 Level: beginner 381 382 Note: 383 Users should never set `PC_MG_GALERKIN_EXTERNAL`, it is used by `PCHYPRE` and `PCML` 384 385 .seealso: [](sec_pc), `PCMG`, `PC`, `PCMGSetCycleType()` 386 E*/ 387 typedef enum { 388 PC_MG_GALERKIN_BOTH, 389 PC_MG_GALERKIN_PMAT, 390 PC_MG_GALERKIN_MAT, 391 PC_MG_GALERKIN_NONE, 392 PC_MG_GALERKIN_EXTERNAL 393 } PCMGGalerkinType; 394 395 /*E 396 PCExoticType - Face based or wirebasket based coarse grid space 397 398 Level: beginner 399 400 .seealso: [](sec_pc), `PCExoticSetType()`, `PCEXOTIC` 401 E*/ 402 typedef enum { 403 PC_EXOTIC_FACE, 404 PC_EXOTIC_WIREBASKET 405 } PCExoticType; 406 407 /*E 408 PCBDDCInterfaceExtType - Defines how interface balancing is extended into the interior of subdomains. 409 410 Values: 411 + `PC_BDDC_INTERFACE_EXT_DIRICHLET` - solves Dirichlet interior problem; this is the standard BDDC algorithm 412 - `PC_BDDC_INTERFACE_EXT_LUMP` - skips interior solve; sometimes called M_1 and associated with "lumped FETI-DP" 413 414 Level: intermediate 415 416 .seealso: [](sec_pc), `PCBDDC`, `PC` 417 E*/ 418 typedef enum { 419 PC_BDDC_INTERFACE_EXT_DIRICHLET, 420 PC_BDDC_INTERFACE_EXT_LUMP 421 } PCBDDCInterfaceExtType; 422 423 /*E 424 PCMGCoarseSpaceType - Function space for coarse space for adaptive interpolation 425 426 Level: beginner 427 428 .seealso: [](sec_pc), `PCMGSetAdaptCoarseSpaceType()`, `PCMG`, `PC` 429 E*/ 430 typedef enum { 431 PCMG_ADAPT_NONE, 432 PCMG_ADAPT_POLYNOMIAL, 433 PCMG_ADAPT_HARMONIC, 434 PCMG_ADAPT_EIGENVECTOR, 435 PCMG_ADAPT_GENERALIZED_EIGENVECTOR, 436 PCMG_ADAPT_GDSW 437 } PCMGCoarseSpaceType; 438 439 /*E 440 PCPatchConstructType - The algorithm used to construct patches for the `PCPATCH` preconditioner 441 442 Level: beginner 443 444 .seealso: [](sec_pc), `PCPatchSetConstructType()`, `PCPATCH`, `PC` 445 E*/ 446 typedef enum { 447 PC_PATCH_STAR, 448 PC_PATCH_VANKA, 449 PC_PATCH_PARDECOMP, 450 PC_PATCH_USER, 451 PC_PATCH_PYTHON 452 } PCPatchConstructType; 453 454 /*E 455 PCDeflationSpaceType - Type of deflation 456 457 Values: 458 + `PC_DEFLATION_SPACE_HAAR` - directly assembled based on Haar (db2) wavelet with overflowed filter cuted-off 459 . `PC_DEFLATION_SPACE_DB2` - `MATCOMPOSITE` of 1-lvl matices based on db2 (2 coefficient Daubechies / Haar wavelet) 460 . `PC_DEFLATION_SPACE_DB4` - same as above, but with db4 (4 coefficient Daubechies) 461 . `PC_DEFLATION_SPACE_DB8` - same as above, but with db8 (8 coefficient Daubechies) 462 . `PC_DEFLATION_SPACE_DB16` - same as above, but with db16 (16 coefficient Daubechies) 463 . `PC_DEFLATION_SPACE_BIORTH22` - same as above, but with biorthogonal 2.2 (6 coefficients) 464 . `PC_DEFLATION_SPACE_MEYER` - same as above, but with Meyer/FIR (62 coefficients) 465 . `PC_DEFLATION_SPACE_AGGREGATION` - aggregates local indices (given by operator matrix distribution) into a subdomain 466 - `PC_DEFLATION_SPACE_USER` - indicates space set by user 467 468 Level: intermediate 469 470 Note: 471 Wavelet-based space (except Haar) can be used in multilevel deflation. 472 473 .seealso: [](sec_pc), `PCDeflationSetSpaceToCompute()`, `PCDEFLATION`, `PC` 474 E*/ 475 typedef enum { 476 PC_DEFLATION_SPACE_HAAR, 477 PC_DEFLATION_SPACE_DB2, 478 PC_DEFLATION_SPACE_DB4, 479 PC_DEFLATION_SPACE_DB8, 480 PC_DEFLATION_SPACE_DB16, 481 PC_DEFLATION_SPACE_BIORTH22, 482 PC_DEFLATION_SPACE_MEYER, 483 PC_DEFLATION_SPACE_AGGREGATION, 484 PC_DEFLATION_SPACE_USER 485 } PCDeflationSpaceType; 486 487 /*E 488 PCHPDDMCoarseCorrectionType - Type of coarse correction used by `PCHPDDM` 489 490 Values: 491 + `PC_HPDDM_COARSE_CORRECTION_DEFLATED` (default) - eq. (1) in `PCHPDDMShellApply()` 492 . `PC_HPDDM_COARSE_CORRECTION_ADDITIVE` - eq. (2) 493 . `PC_HPDDM_COARSE_CORRECTION_BALANCED` - eq. (3) 494 - `PC_HPDDM_COARSE_CORRECTION_NONE` - no coarse correction (mostly useful for debugging) 495 496 Level: intermediate 497 498 .seealso: [](sec_pc), `PCHPDDM`, `PC`, `PCSetType()`, `PCHPDDMShellApply()` 499 E*/ 500 typedef enum { 501 PC_HPDDM_COARSE_CORRECTION_DEFLATED, 502 PC_HPDDM_COARSE_CORRECTION_ADDITIVE, 503 PC_HPDDM_COARSE_CORRECTION_BALANCED, 504 PC_HPDDM_COARSE_CORRECTION_NONE 505 } PCHPDDMCoarseCorrectionType; 506 507 /*E 508 PCHPDDMSchurPreType - Type of `PCHPDDM` preconditioner for a `MATSCHURCOMPLEMENT` generated by `PCFIELDSPLIT` with `PCFieldSplitSchurPreType` set to `PC_FIELDSPLIT_SCHUR_PRE_SELF` 509 510 Values: 511 + `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 512 - `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 513 514 Level: advanced 515 516 .seealso: [](sec_pc), `PCHPDDM`, `PC`, `PCFIELDSPLIT`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PCFieldSplitSetSchurPre()`, `PCHPDDMSetAuxiliaryMat()` 517 E*/ 518 typedef enum { 519 PC_HPDDM_SCHUR_PRE_LEAST_SQUARES, 520 PC_HPDDM_SCHUR_PRE_GENEO, 521 } PCHPDDMSchurPreType; 522 523 /*E 524 PCFailedReason - indicates type of `PC` failure 525 526 Level: beginner 527 528 .seealso: [](sec_pc), `PC` 529 E*/ 530 typedef enum { 531 PC_SETUP_ERROR = -1, 532 PC_NOERROR, 533 PC_FACTOR_STRUCT_ZEROPIVOT, 534 PC_FACTOR_NUMERIC_ZEROPIVOT, 535 PC_FACTOR_OUTMEMORY, 536 PC_FACTOR_OTHER, 537 PC_INCONSISTENT_RHS, 538 PC_SUBPC_ERROR 539 } PCFailedReason; 540 541 /*E 542 PCGAMGLayoutType - Layout for reduced grids 543 544 Level: intermediate 545 546 .seealso: [](sec_pc), `PCGAMG`, `PC`, `PCGAMGSetCoarseGridLayoutType()` 547 E*/ 548 typedef enum { 549 PCGAMG_LAYOUT_COMPACT, 550 PCGAMG_LAYOUT_SPREAD 551 } PCGAMGLayoutType; 552