1*7f296bb3SBarry Smith(doc_linsolve)= 2*7f296bb3SBarry Smith 3*7f296bb3SBarry Smith# Summary of Sparse Linear Solvers Available In PETSc 4*7f296bb3SBarry Smith 5*7f296bb3SBarry Smith## Preconditioners 6*7f296bb3SBarry Smith 7*7f296bb3SBarry Smith```{eval-rst} 8*7f296bb3SBarry Smith.. list-table:: 9*7f296bb3SBarry Smith :widths: auto 10*7f296bb3SBarry Smith :align: center 11*7f296bb3SBarry Smith :header-rows: 1 12*7f296bb3SBarry Smith 13*7f296bb3SBarry Smith * - 14*7f296bb3SBarry Smith - Algorithm 15*7f296bb3SBarry Smith - Associated Type 16*7f296bb3SBarry Smith - Matrix Types 17*7f296bb3SBarry Smith - External Packages 18*7f296bb3SBarry Smith - Parallel 19*7f296bb3SBarry Smith - Complex 20*7f296bb3SBarry Smith * - Generic 21*7f296bb3SBarry Smith - Jacobi 22*7f296bb3SBarry Smith - ``PCJACOBI`` 23*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ``, ``MATDENSE`` 24*7f296bb3SBarry Smith - --- 25*7f296bb3SBarry Smith - X 26*7f296bb3SBarry Smith - X 27*7f296bb3SBarry Smith * - 28*7f296bb3SBarry Smith - Point Block Jacobi 29*7f296bb3SBarry Smith - ``PCPBJACOBI`` 30*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ``, ``MATKAIJ``, ``MATMPISELL``, ``MATIS`` 31*7f296bb3SBarry Smith - --- 32*7f296bb3SBarry Smith - X 33*7f296bb3SBarry Smith - X 34*7f296bb3SBarry Smith * - 35*7f296bb3SBarry Smith - Variable Point Block Jacobi 36*7f296bb3SBarry Smith - ``PCPBJACOBI`` 37*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ`` 38*7f296bb3SBarry Smith - --- 39*7f296bb3SBarry Smith - X 40*7f296bb3SBarry Smith - X 41*7f296bb3SBarry Smith * - 42*7f296bb3SBarry Smith - Block Jacobi 43*7f296bb3SBarry Smith - ``PCBJACOBI`` 44*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ`` 45*7f296bb3SBarry Smith - --- 46*7f296bb3SBarry Smith - X 47*7f296bb3SBarry Smith - X 48*7f296bb3SBarry Smith * - 49*7f296bb3SBarry Smith - SOR 50*7f296bb3SBarry Smith - ``PCSOR`` 51*7f296bb3SBarry Smith - ``MATAIJ``, ``MATSEQDENSE``, ``MATSEQSBAIJ`` 52*7f296bb3SBarry Smith - --- 53*7f296bb3SBarry Smith - X 54*7f296bb3SBarry Smith - X 55*7f296bb3SBarry Smith * - 56*7f296bb3SBarry Smith - Point Block SOR 57*7f296bb3SBarry Smith - 58*7f296bb3SBarry Smith - ``MATSEQBAIJ`` (only for ``bs`` = 2,3,4,5) 59*7f296bb3SBarry Smith - --- 60*7f296bb3SBarry Smith - X 61*7f296bb3SBarry Smith - X 62*7f296bb3SBarry Smith * - 63*7f296bb3SBarry Smith - Kaczmarz 64*7f296bb3SBarry Smith - ``PCKACZMARZ`` 65*7f296bb3SBarry Smith - ``MATAIJ`` 66*7f296bb3SBarry Smith - --- 67*7f296bb3SBarry Smith - X 68*7f296bb3SBarry Smith - X 69*7f296bb3SBarry Smith * - 70*7f296bb3SBarry Smith - Additive Schwarz 71*7f296bb3SBarry Smith - ``PCASM`` 72*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ`` 73*7f296bb3SBarry Smith - --- 74*7f296bb3SBarry Smith - X 75*7f296bb3SBarry Smith - X 76*7f296bb3SBarry Smith * - 77*7f296bb3SBarry Smith - Vanka/overlapping patches 78*7f296bb3SBarry Smith - ``PCPATCH`` 79*7f296bb3SBarry Smith - ``MATAIJ`` 80*7f296bb3SBarry Smith - --- 81*7f296bb3SBarry Smith - X 82*7f296bb3SBarry Smith - X 83*7f296bb3SBarry Smith * - 84*7f296bb3SBarry Smith - Deflation 85*7f296bb3SBarry Smith - ``PCDEFLATION`` 86*7f296bb3SBarry Smith - All 87*7f296bb3SBarry Smith - --- 88*7f296bb3SBarry Smith - X 89*7f296bb3SBarry Smith - X 90*7f296bb3SBarry Smith * - Incomplete 91*7f296bb3SBarry Smith - ILU 92*7f296bb3SBarry Smith - ``PCILU`` 93*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQBAIJ`` 94*7f296bb3SBarry Smith - --- 95*7f296bb3SBarry Smith - 96*7f296bb3SBarry Smith - X 97*7f296bb3SBarry Smith * - 98*7f296bb3SBarry Smith - ILU with drop tolerance 99*7f296bb3SBarry Smith - ``PCILU`` 100*7f296bb3SBarry Smith - ``MATSEQAIJ`` 101*7f296bb3SBarry Smith - `SuperLU Sequential ILU solver 102*7f296bb3SBarry Smith <../../manualpages/Mat/MATSOLVERSUPERLU.html>`__ 103*7f296bb3SBarry Smith - 104*7f296bb3SBarry Smith - X 105*7f296bb3SBarry Smith * - 106*7f296bb3SBarry Smith - 107*7f296bb3SBarry Smith - ``PCILU`` 108*7f296bb3SBarry Smith - ``MATAIJ`` 109*7f296bb3SBarry Smith - Euclid/hypre (``PCHYPRE``) 110*7f296bb3SBarry Smith - X 111*7f296bb3SBarry Smith - 112*7f296bb3SBarry Smith * - 113*7f296bb3SBarry Smith - ICholesky 114*7f296bb3SBarry Smith - ``PCICC`` 115*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQBAIJ``, ``MATSEQSBAIJ`` 116*7f296bb3SBarry Smith - --- 117*7f296bb3SBarry Smith - 118*7f296bb3SBarry Smith - X 119*7f296bb3SBarry Smith * - 120*7f296bb3SBarry Smith - Algebraic recursive multilevel 121*7f296bb3SBarry Smith - ``PCPARMS`` 122*7f296bb3SBarry Smith - ``MATSEQAIJ`` 123*7f296bb3SBarry Smith - `pARMS <https://www-users.cse.umn.edu/~saad/software/pARMS/>`__ 124*7f296bb3SBarry Smith - 125*7f296bb3SBarry Smith - X 126*7f296bb3SBarry Smith * - Matrix Free 127*7f296bb3SBarry Smith - Infrastructure 128*7f296bb3SBarry Smith - ``PCSHELL`` 129*7f296bb3SBarry Smith - All 130*7f296bb3SBarry Smith - --- 131*7f296bb3SBarry Smith - X 132*7f296bb3SBarry Smith - X 133*7f296bb3SBarry Smith * - Multigrid 134*7f296bb3SBarry Smith - Infrastructure 135*7f296bb3SBarry Smith - ``PCMG`` 136*7f296bb3SBarry Smith - All 137*7f296bb3SBarry Smith - --- 138*7f296bb3SBarry Smith - X 139*7f296bb3SBarry Smith - X 140*7f296bb3SBarry Smith * - 141*7f296bb3SBarry Smith - Geometric 142*7f296bb3SBarry Smith - 143*7f296bb3SBarry Smith - All 144*7f296bb3SBarry Smith - --- 145*7f296bb3SBarry Smith - X 146*7f296bb3SBarry Smith - X 147*7f296bb3SBarry Smith * - 148*7f296bb3SBarry Smith - Smoothed Aggregation 149*7f296bb3SBarry Smith - ``PCGAMG`` 150*7f296bb3SBarry Smith - ``MATAIJ`` 151*7f296bb3SBarry Smith - --- 152*7f296bb3SBarry Smith - X 153*7f296bb3SBarry Smith - X 154*7f296bb3SBarry Smith * - 155*7f296bb3SBarry Smith - Smoothed Aggregation (ML) 156*7f296bb3SBarry Smith - ``PCML`` 157*7f296bb3SBarry Smith - ``MATAIJ`` 158*7f296bb3SBarry Smith - `ML/Trilinos <https://trilinos.github.io/ml.html>`__ 159*7f296bb3SBarry Smith - X 160*7f296bb3SBarry Smith - X 161*7f296bb3SBarry Smith * - 162*7f296bb3SBarry Smith - Structured Geometric 163*7f296bb3SBarry Smith - ``PCPFMG``, ``PCSYSPFMG``, ``PCSMG`` 164*7f296bb3SBarry Smith - ``MATHYPRESTRUCT`` 165*7f296bb3SBarry Smith - `hypre <https://hypre.readthedocs.io/en/latest/solvers-smg-pfmg.html>`__ 166*7f296bb3SBarry Smith - X 167*7f296bb3SBarry Smith - 168*7f296bb3SBarry Smith * - 169*7f296bb3SBarry Smith - Classical Algebraic 170*7f296bb3SBarry Smith - ``PCHYPRE``, ``PCAMGX`` 171*7f296bb3SBarry Smith - ``MATAIJ`` 172*7f296bb3SBarry Smith - `BoomerAMG/hypre 173*7f296bb3SBarry Smith <https://hypre.readthedocs.io/en/latest/solvers-boomeramg.html>`__, `AmgX <https://developer.nvidia.com/amgx>`__ 174*7f296bb3SBarry Smith - X 175*7f296bb3SBarry Smith - 176*7f296bb3SBarry Smith * - 177*7f296bb3SBarry Smith - Multi-group MG 178*7f296bb3SBarry Smith - ``PCHMG`` 179*7f296bb3SBarry Smith - ``MATAIJ`` 180*7f296bb3SBarry Smith - --- 181*7f296bb3SBarry Smith - X 182*7f296bb3SBarry Smith - X 183*7f296bb3SBarry Smith * - 184*7f296bb3SBarry Smith - Domain Decomposition 185*7f296bb3SBarry Smith - ``PCHPDDM`` 186*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSBAIJ``, ``MATIS`` 187*7f296bb3SBarry Smith - `HPDDM <https://github.com/hpddm/hpddm>`__ 188*7f296bb3SBarry Smith - X 189*7f296bb3SBarry Smith - X 190*7f296bb3SBarry Smith * - Hierarchical matrices 191*7f296bb3SBarry Smith - :math:`\mathcal H^2` 192*7f296bb3SBarry Smith - ``PCH2OPUS`` 193*7f296bb3SBarry Smith - ``MATHTOOL``, ``MATH2OPUS`` 194*7f296bb3SBarry Smith - `H2OPUS <https://github.com/ecrc/h2opus>`__ 195*7f296bb3SBarry Smith - X 196*7f296bb3SBarry Smith - 197*7f296bb3SBarry Smith * - Physics-based Splitting 198*7f296bb3SBarry Smith - Relaxation & Schur Complement 199*7f296bb3SBarry Smith - ``PCFIELDSPLIT`` 200*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATNEST`` 201*7f296bb3SBarry Smith - --- 202*7f296bb3SBarry Smith - X 203*7f296bb3SBarry Smith - X 204*7f296bb3SBarry Smith * - 205*7f296bb3SBarry Smith - Galerkin composition 206*7f296bb3SBarry Smith - ``PCGALERKIN`` 207*7f296bb3SBarry Smith - Any 208*7f296bb3SBarry Smith - --- 209*7f296bb3SBarry Smith - X 210*7f296bb3SBarry Smith - X 211*7f296bb3SBarry Smith * - 212*7f296bb3SBarry Smith - Additive/multiplicative 213*7f296bb3SBarry Smith - ``PCCOMPOSITE`` 214*7f296bb3SBarry Smith - Any 215*7f296bb3SBarry Smith - --- 216*7f296bb3SBarry Smith - X 217*7f296bb3SBarry Smith - X 218*7f296bb3SBarry Smith * - 219*7f296bb3SBarry Smith - Least Squares Commutator 220*7f296bb3SBarry Smith - ``PCLSC`` 221*7f296bb3SBarry Smith - ``MATSCHURCOMPLEMENT`` 222*7f296bb3SBarry Smith - --- 223*7f296bb3SBarry Smith - X 224*7f296bb3SBarry Smith - X 225*7f296bb3SBarry Smith * - Parallel transformation 226*7f296bb3SBarry Smith - Redistribution 227*7f296bb3SBarry Smith - ``PCREDISTRIBUTE`` 228*7f296bb3SBarry Smith - ``MATAIJ`` 229*7f296bb3SBarry Smith - --- 230*7f296bb3SBarry Smith - X 231*7f296bb3SBarry Smith - X 232*7f296bb3SBarry Smith * - 233*7f296bb3SBarry Smith - Telescoping communicator 234*7f296bb3SBarry Smith - ``PCTELESCOPE`` 235*7f296bb3SBarry Smith - ``MATAIJ`` 236*7f296bb3SBarry Smith - --- 237*7f296bb3SBarry Smith - X 238*7f296bb3SBarry Smith - X 239*7f296bb3SBarry Smith * - 240*7f296bb3SBarry Smith - Distribute for MPI 241*7f296bb3SBarry Smith - ``PCMPI`` 242*7f296bb3SBarry Smith - ``MATAIJ`` 243*7f296bb3SBarry Smith - --- 244*7f296bb3SBarry Smith - X 245*7f296bb3SBarry Smith - X 246*7f296bb3SBarry Smith * - Approximate Inverse 247*7f296bb3SBarry Smith - AIV 248*7f296bb3SBarry Smith - ``PCHYPRE``, ``PCSPAI`` 249*7f296bb3SBarry Smith - ``MATAIJ`` 250*7f296bb3SBarry Smith - `Parasails/hypre <https://hypre.readthedocs.io/en/latest/solvers-parasails.html>`__, `SPAI <https://epubs.siam.org/doi/abs/10.1137/S1064827595294691?journalCode=sjoce3>`__ 251*7f296bb3SBarry Smith - X 252*7f296bb3SBarry Smith - 253*7f296bb3SBarry Smith * - Substructuring 254*7f296bb3SBarry Smith - Balancing Neumann-Neumann 255*7f296bb3SBarry Smith - ``PCNN`` 256*7f296bb3SBarry Smith - ``MATIS`` 257*7f296bb3SBarry Smith - --- 258*7f296bb3SBarry Smith - X 259*7f296bb3SBarry Smith - X 260*7f296bb3SBarry Smith * - 261*7f296bb3SBarry Smith - Balancing Domain Decomposition 262*7f296bb3SBarry Smith - ``PCBDDC`` 263*7f296bb3SBarry Smith - ``MATIS`` 264*7f296bb3SBarry Smith - --- 265*7f296bb3SBarry Smith - X 266*7f296bb3SBarry Smith - X 267*7f296bb3SBarry Smith * - 268*7f296bb3SBarry Smith - 2-level Schwarz wire basket 269*7f296bb3SBarry Smith - ``PCEXOTIC`` 270*7f296bb3SBarry Smith - ``MATAIJ`` 271*7f296bb3SBarry Smith - --- 272*7f296bb3SBarry Smith - X 273*7f296bb3SBarry Smith - X 274*7f296bb3SBarry Smith``` 275*7f296bb3SBarry Smith 276*7f296bb3SBarry Smith______________________________________________________________________ 277*7f296bb3SBarry Smith 278*7f296bb3SBarry Smith## Direct Solvers 279*7f296bb3SBarry Smith 280*7f296bb3SBarry Smith```{eval-rst} 281*7f296bb3SBarry Smith.. list-table:: 282*7f296bb3SBarry Smith :widths: auto 283*7f296bb3SBarry Smith :align: center 284*7f296bb3SBarry Smith :header-rows: 1 285*7f296bb3SBarry Smith 286*7f296bb3SBarry Smith * - 287*7f296bb3SBarry Smith - Algorithm 288*7f296bb3SBarry Smith - Associated Type 289*7f296bb3SBarry Smith - Matrix Types 290*7f296bb3SBarry Smith - External Packages 291*7f296bb3SBarry Smith - Parallel 292*7f296bb3SBarry Smith - Complex 293*7f296bb3SBarry Smith * - Direct LU 294*7f296bb3SBarry Smith - LU 295*7f296bb3SBarry Smith - ``PCLU`` 296*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQBAIJ`` 297*7f296bb3SBarry Smith - --- 298*7f296bb3SBarry Smith - 299*7f296bb3SBarry Smith - X 300*7f296bb3SBarry Smith * - 301*7f296bb3SBarry Smith - 302*7f296bb3SBarry Smith - 303*7f296bb3SBarry Smith - ``MATSEQAIJ`` 304*7f296bb3SBarry Smith - `MATLAB <https://www.mathworks.com/products/matlab.html>`__ 305*7f296bb3SBarry Smith - 306*7f296bb3SBarry Smith - X 307*7f296bb3SBarry Smith * - 308*7f296bb3SBarry Smith - 309*7f296bb3SBarry Smith - 310*7f296bb3SBarry Smith - ``MATAIJ`` 311*7f296bb3SBarry Smith - `PaStiX <http://pastix.gforge.inria.fr/files/README-txt.html>`__ 312*7f296bb3SBarry Smith - X 313*7f296bb3SBarry Smith - X 314*7f296bb3SBarry Smith * - 315*7f296bb3SBarry Smith - 316*7f296bb3SBarry Smith - 317*7f296bb3SBarry Smith - ``MATAIJ`` 318*7f296bb3SBarry Smith - `SuperLU <https://portal.nersc.gov/project/sparse/superlu/>`__ 319*7f296bb3SBarry Smith - X 320*7f296bb3SBarry Smith - X 321*7f296bb3SBarry Smith * - 322*7f296bb3SBarry Smith - 323*7f296bb3SBarry Smith - 324*7f296bb3SBarry Smith - ``MATAIJ``, ``MATBAIJ``, ``MATSEQSELL``, ``MATDENSE``, ``MATNEST`` 325*7f296bb3SBarry Smith - `MUMPS <https://mumps-solver.org/>`__ 326*7f296bb3SBarry Smith - X 327*7f296bb3SBarry Smith - X 328*7f296bb3SBarry Smith * - 329*7f296bb3SBarry Smith - 330*7f296bb3SBarry Smith - 331*7f296bb3SBarry Smith - ``MATSEQAIJ`` 332*7f296bb3SBarry Smith - `ESSL <https://www.ibm.com/support/knowledgecenter/en/SSFHY8/essl_welcome.html>`__ 333*7f296bb3SBarry Smith - 334*7f296bb3SBarry Smith - 335*7f296bb3SBarry Smith * - 336*7f296bb3SBarry Smith - 337*7f296bb3SBarry Smith - 338*7f296bb3SBarry Smith - ``MATSEQAIJ`` 339*7f296bb3SBarry Smith - `UMFPACK (SuiteSparse) <https://people.engr.tamu.edu/davis/suitesparse.html>`__ 340*7f296bb3SBarry Smith - 341*7f296bb3SBarry Smith - X 342*7f296bb3SBarry Smith * - 343*7f296bb3SBarry Smith - 344*7f296bb3SBarry Smith - 345*7f296bb3SBarry Smith - ``MATSEQAIJ`` 346*7f296bb3SBarry Smith - `KLU (SuiteSparse) <https://people.engr.tamu.edu/davis/suitesparse.html>`__ 347*7f296bb3SBarry Smith - 348*7f296bb3SBarry Smith - X 349*7f296bb3SBarry Smith * - 350*7f296bb3SBarry Smith - 351*7f296bb3SBarry Smith - 352*7f296bb3SBarry Smith - ``MATSEQAIJ`` 353*7f296bb3SBarry Smith - `LUSOL <https://web.stanford.edu/group/SOL/software/lusol/>`__ 354*7f296bb3SBarry Smith - 355*7f296bb3SBarry Smith - 356*7f296bb3SBarry Smith * - 357*7f296bb3SBarry Smith - 358*7f296bb3SBarry Smith - 359*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQBAIJ`` 360*7f296bb3SBarry Smith - `MKL PARDISO 361*7f296bb3SBarry Smith <https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html>`__ 362*7f296bb3SBarry Smith - 363*7f296bb3SBarry Smith - X 364*7f296bb3SBarry Smith * - 365*7f296bb3SBarry Smith - 366*7f296bb3SBarry Smith - 367*7f296bb3SBarry Smith - ``MATMPIAIJ``, ``MATMPIBAIJ`` 368*7f296bb3SBarry Smith - `MKL Cluster PARDISO 369*7f296bb3SBarry Smith <https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html>`__ 370*7f296bb3SBarry Smith - X 371*7f296bb3SBarry Smith - X 372*7f296bb3SBarry Smith * - 373*7f296bb3SBarry Smith - 374*7f296bb3SBarry Smith - 375*7f296bb3SBarry Smith - ``MATDENSE`` 376*7f296bb3SBarry Smith - `Elemental <https://github.com/elemental/Elemental>`__ 377*7f296bb3SBarry Smith - X 378*7f296bb3SBarry Smith - X 379*7f296bb3SBarry Smith * - Direct Cholesky 380*7f296bb3SBarry Smith - Cholesky 381*7f296bb3SBarry Smith - ``PCCHOLESKY`` 382*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQSBAIJ`` 383*7f296bb3SBarry Smith - --- 384*7f296bb3SBarry Smith - 385*7f296bb3SBarry Smith - X 386*7f296bb3SBarry Smith * - 387*7f296bb3SBarry Smith - 388*7f296bb3SBarry Smith - 389*7f296bb3SBarry Smith - ``MATSBAIJ`` 390*7f296bb3SBarry Smith - `PaStiX <http://pastix.gforge.inria.fr/files/README-txt.html>`__ 391*7f296bb3SBarry Smith - X 392*7f296bb3SBarry Smith - X 393*7f296bb3SBarry Smith * - 394*7f296bb3SBarry Smith - 395*7f296bb3SBarry Smith - 396*7f296bb3SBarry Smith - ``MATAIJ``, ``MATSBAIJ``, ``MATDENSE``, ``MATNEST`` 397*7f296bb3SBarry Smith - `MUMPS <https://mumps-solver.org/>`__ 398*7f296bb3SBarry Smith - X 399*7f296bb3SBarry Smith - X 400*7f296bb3SBarry Smith * - 401*7f296bb3SBarry Smith - 402*7f296bb3SBarry Smith - 403*7f296bb3SBarry Smith - ``MATSEQAIJ``, ``MATSEQSBAIJ`` 404*7f296bb3SBarry Smith - `CHOLMOD (SuiteSparse) <https://people.engr.tamu.edu/davis/suitesparse.html>`__ 405*7f296bb3SBarry Smith - 406*7f296bb3SBarry Smith - X 407*7f296bb3SBarry Smith * - 408*7f296bb3SBarry Smith - 409*7f296bb3SBarry Smith - 410*7f296bb3SBarry Smith - ``MATDENSE`` 411*7f296bb3SBarry Smith - `Elemental <https://github.com/elemental/Elemental>`__ 412*7f296bb3SBarry Smith - X 413*7f296bb3SBarry Smith - X 414*7f296bb3SBarry Smith * - 415*7f296bb3SBarry Smith - 416*7f296bb3SBarry Smith - 417*7f296bb3SBarry Smith - ``MATSEQSBAIJ`` 418*7f296bb3SBarry Smith - `MKL PARDISO 419*7f296bb3SBarry Smith <https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html>`__ 420*7f296bb3SBarry Smith - 421*7f296bb3SBarry Smith - 422*7f296bb3SBarry Smith * - 423*7f296bb3SBarry Smith - 424*7f296bb3SBarry Smith - 425*7f296bb3SBarry Smith - ``MATMPIAIJ``, ``MATMPIBAIJ`` 426*7f296bb3SBarry Smith - `MKL CPardiso 427*7f296bb3SBarry Smith <https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html>`__ 428*7f296bb3SBarry Smith - X 429*7f296bb3SBarry Smith - 430*7f296bb3SBarry Smith * - Direct SVD 431*7f296bb3SBarry Smith - Singular value decomposition 432*7f296bb3SBarry Smith - ``PCSVD`` 433*7f296bb3SBarry Smith - Any 434*7f296bb3SBarry Smith - --- 435*7f296bb3SBarry Smith - X 436*7f296bb3SBarry Smith - X 437*7f296bb3SBarry Smith * - Direct QR 438*7f296bb3SBarry Smith - QR 439*7f296bb3SBarry Smith - ``PCQR`` 440*7f296bb3SBarry Smith - ``MATSEQAIJ`` 441*7f296bb3SBarry Smith - `SuiteSparse QR <https://people.engr.tamu.edu/davis/suitesparse.html>`__ 442*7f296bb3SBarry Smith - 443*7f296bb3SBarry Smith - 444*7f296bb3SBarry Smith * - 445*7f296bb3SBarry Smith - XXt and XYt 446*7f296bb3SBarry Smith - 447*7f296bb3SBarry Smith - ``MATAIJ`` 448*7f296bb3SBarry Smith - --- 449*7f296bb3SBarry Smith - X 450*7f296bb3SBarry Smith - 451*7f296bb3SBarry Smith``` 452*7f296bb3SBarry Smith 453*7f296bb3SBarry Smith______________________________________________________________________ 454*7f296bb3SBarry Smith 455*7f296bb3SBarry Smith## Krylov Methods 456*7f296bb3SBarry Smith 457*7f296bb3SBarry Smith```{eval-rst} 458*7f296bb3SBarry Smith.. list-table:: 459*7f296bb3SBarry Smith :widths: auto 460*7f296bb3SBarry Smith :align: center 461*7f296bb3SBarry Smith :header-rows: 1 462*7f296bb3SBarry Smith 463*7f296bb3SBarry Smith * - Algorithm 464*7f296bb3SBarry Smith - Associated Type 465*7f296bb3SBarry Smith - External Packages 466*7f296bb3SBarry Smith - Parallel 467*7f296bb3SBarry Smith - Complex 468*7f296bb3SBarry Smith * - Richardson 469*7f296bb3SBarry Smith - ``KSPRICHARDSON`` 470*7f296bb3SBarry Smith - --- 471*7f296bb3SBarry Smith - X 472*7f296bb3SBarry Smith - X 473*7f296bb3SBarry Smith * - Chebyshev 474*7f296bb3SBarry Smith - ``KSPCHEBYSHEV`` 475*7f296bb3SBarry Smith - --- 476*7f296bb3SBarry Smith - X 477*7f296bb3SBarry Smith - X 478*7f296bb3SBarry Smith * - GMRES 479*7f296bb3SBarry Smith - ``KSPGMRES`` 480*7f296bb3SBarry Smith - --- 481*7f296bb3SBarry Smith - X 482*7f296bb3SBarry Smith - X 483*7f296bb3SBarry Smith * - Flexible GMRES 484*7f296bb3SBarry Smith - ``KSPFGMRES`` 485*7f296bb3SBarry Smith - --- 486*7f296bb3SBarry Smith - X 487*7f296bb3SBarry Smith - X 488*7f296bb3SBarry Smith * - LGMRES 489*7f296bb3SBarry Smith - ``KSPLGMRES`` 490*7f296bb3SBarry Smith - --- 491*7f296bb3SBarry Smith - X 492*7f296bb3SBarry Smith - X 493*7f296bb3SBarry Smith * - Deflated GMRES 494*7f296bb3SBarry Smith - ``KSPDGMRES`` 495*7f296bb3SBarry Smith - --- 496*7f296bb3SBarry Smith - X 497*7f296bb3SBarry Smith - 498*7f296bb3SBarry Smith * - Two-stage with least squares residual minimization 499*7f296bb3SBarry Smith - ``KSPTSIRM`` 500*7f296bb3SBarry Smith - --- 501*7f296bb3SBarry Smith - X 502*7f296bb3SBarry Smith - X 503*7f296bb3SBarry Smith * - Conjugate Gradient 504*7f296bb3SBarry Smith - ``KSPCG`` 505*7f296bb3SBarry Smith - --- 506*7f296bb3SBarry Smith - X 507*7f296bb3SBarry Smith - X 508*7f296bb3SBarry Smith * - Conjugate Gradient Squared 509*7f296bb3SBarry Smith - ``KSPCGS`` 510*7f296bb3SBarry Smith - --- 511*7f296bb3SBarry Smith - X 512*7f296bb3SBarry Smith - X 513*7f296bb3SBarry Smith * - Conjugate Gradient for Least Squares 514*7f296bb3SBarry Smith - ``KSPCGLS`` 515*7f296bb3SBarry Smith - --- 516*7f296bb3SBarry Smith - X 517*7f296bb3SBarry Smith - X 518*7f296bb3SBarry Smith * - Conjugate Gradient on Normal Equations 519*7f296bb3SBarry Smith - ``KSPCGNE`` 520*7f296bb3SBarry Smith - --- 521*7f296bb3SBarry Smith - X 522*7f296bb3SBarry Smith - X 523*7f296bb3SBarry Smith * - Nash Conjugate Gradient with trust region constraint 524*7f296bb3SBarry Smith - ``KSPNASH`` 525*7f296bb3SBarry Smith - --- 526*7f296bb3SBarry Smith - X 527*7f296bb3SBarry Smith - X 528*7f296bb3SBarry Smith * - Conjugate Gradient with trust region constraint 529*7f296bb3SBarry Smith - ``KSPSTCG`` 530*7f296bb3SBarry Smith - --- 531*7f296bb3SBarry Smith - X 532*7f296bb3SBarry Smith - X 533*7f296bb3SBarry Smith * - Gould et al Conjugate Gradient with trust region constraint 534*7f296bb3SBarry Smith - ``KSPGLTR`` 535*7f296bb3SBarry Smith - --- 536*7f296bb3SBarry Smith - X 537*7f296bb3SBarry Smith - X 538*7f296bb3SBarry Smith * - Steinhaug Conjugate Gradient with trust region constraint 539*7f296bb3SBarry Smith - ``KSPQCG`` 540*7f296bb3SBarry Smith - --- 541*7f296bb3SBarry Smith - X 542*7f296bb3SBarry Smith - X 543*7f296bb3SBarry Smith * - Left Conjugate Direction 544*7f296bb3SBarry Smith - ``KSPLCD`` 545*7f296bb3SBarry Smith - --- 546*7f296bb3SBarry Smith - X 547*7f296bb3SBarry Smith - X 548*7f296bb3SBarry Smith * - Bi-Conjugate Gradient 549*7f296bb3SBarry Smith - ``KSPBICG`` 550*7f296bb3SBarry Smith - --- 551*7f296bb3SBarry Smith - X 552*7f296bb3SBarry Smith - X 553*7f296bb3SBarry Smith * - Stabilized Bi-Conjugate Gradient 554*7f296bb3SBarry Smith - ``KSPBCGS`` 555*7f296bb3SBarry Smith - --- 556*7f296bb3SBarry Smith - X 557*7f296bb3SBarry Smith - X 558*7f296bb3SBarry Smith * - Improved Stabilized Bi-Conjugate Gradient 559*7f296bb3SBarry Smith - ``KSPIBCGS`` 560*7f296bb3SBarry Smith - --- 561*7f296bb3SBarry Smith - X 562*7f296bb3SBarry Smith - X 563*7f296bb3SBarry Smith * - Transpose-free QMR 564*7f296bb3SBarry Smith - ``KSPTFQMR`` 565*7f296bb3SBarry Smith - --- 566*7f296bb3SBarry Smith - X 567*7f296bb3SBarry Smith - X 568*7f296bb3SBarry Smith * - Transpose-free variant of QMR developed by Tony Chan 569*7f296bb3SBarry Smith - ``KSPTCQMR`` 570*7f296bb3SBarry Smith - --- 571*7f296bb3SBarry Smith - X 572*7f296bb3SBarry Smith - X 573*7f296bb3SBarry Smith * - QMR BiCGStab 574*7f296bb3SBarry Smith - ``KSPQMRCGS`` 575*7f296bb3SBarry Smith - --- 576*7f296bb3SBarry Smith - X 577*7f296bb3SBarry Smith - X 578*7f296bb3SBarry Smith * - Flexible Conjugate Gradients 579*7f296bb3SBarry Smith - ``KSPFCG`` 580*7f296bb3SBarry Smith - --- 581*7f296bb3SBarry Smith - X 582*7f296bb3SBarry Smith - X 583*7f296bb3SBarry Smith * - Flexible stabilized Bi-Conjugate Gradients 584*7f296bb3SBarry Smith - ``KSPFBCGS`` 585*7f296bb3SBarry Smith - --- 586*7f296bb3SBarry Smith - X 587*7f296bb3SBarry Smith - X 588*7f296bb3SBarry Smith * - Flexible stabilized Bi-Conjugate Gradients with fewer reductions 589*7f296bb3SBarry Smith - ``KSPFBCGSR`` 590*7f296bb3SBarry Smith - --- 591*7f296bb3SBarry Smith - X 592*7f296bb3SBarry Smith - X 593*7f296bb3SBarry Smith * - Stabilized Bi-Conjugate Gradients with length :math:`\ell` recurrence 594*7f296bb3SBarry Smith - ``KSPBCGSL`` 595*7f296bb3SBarry Smith - --- 596*7f296bb3SBarry Smith - X 597*7f296bb3SBarry Smith - X 598*7f296bb3SBarry Smith * - Conjugate Residual 599*7f296bb3SBarry Smith - ``KSPCR`` 600*7f296bb3SBarry Smith - --- 601*7f296bb3SBarry Smith - X 602*7f296bb3SBarry Smith - X 603*7f296bb3SBarry Smith * - Generalized Conjugate Residual 604*7f296bb3SBarry Smith - ``KSPGCR`` 605*7f296bb3SBarry Smith - --- 606*7f296bb3SBarry Smith - X 607*7f296bb3SBarry Smith - X 608*7f296bb3SBarry Smith * - Generalized Conjugate Residual (with inner normalization and deflated restarts) 609*7f296bb3SBarry Smith - ``KSPHPDDM`` 610*7f296bb3SBarry Smith - `HPDDM <https://github.com/hpddm/hpddm>`__ 611*7f296bb3SBarry Smith - X 612*7f296bb3SBarry Smith - X 613*7f296bb3SBarry Smith * - Minimum Residual 614*7f296bb3SBarry Smith - ``KSPMINRES`` 615*7f296bb3SBarry Smith - --- 616*7f296bb3SBarry Smith - X 617*7f296bb3SBarry Smith - X 618*7f296bb3SBarry Smith * - LSQR 619*7f296bb3SBarry Smith - ``KSPLSQR`` 620*7f296bb3SBarry Smith - --- 621*7f296bb3SBarry Smith - X 622*7f296bb3SBarry Smith - X 623*7f296bb3SBarry Smith * - SYMMLQ 624*7f296bb3SBarry Smith - ``KSPSYMMLQ`` 625*7f296bb3SBarry Smith - --- 626*7f296bb3SBarry Smith - X 627*7f296bb3SBarry Smith - X 628*7f296bb3SBarry Smith * - FETI-DP (reduction to dual-primal sub-problem) 629*7f296bb3SBarry Smith - ``KSPFETIDP`` 630*7f296bb3SBarry Smith - --- 631*7f296bb3SBarry Smith - X 632*7f296bb3SBarry Smith - X 633*7f296bb3SBarry Smith * - Gropp's overlapped reduction pipelined Conjugate Gradient 634*7f296bb3SBarry Smith - ``KSPGROPPCG`` 635*7f296bb3SBarry Smith - --- 636*7f296bb3SBarry Smith - X 637*7f296bb3SBarry Smith - X 638*7f296bb3SBarry Smith * - Pipelined Conjugate Gradient 639*7f296bb3SBarry Smith - ``KSPPIPECG`` 640*7f296bb3SBarry Smith - --- 641*7f296bb3SBarry Smith - X 642*7f296bb3SBarry Smith - X 643*7f296bb3SBarry Smith * - Pipelined Conjugate Gradient with residual replacement 644*7f296bb3SBarry Smith - ``KSPPIPECGRR`` 645*7f296bb3SBarry Smith - --- 646*7f296bb3SBarry Smith - X 647*7f296bb3SBarry Smith - X 648*7f296bb3SBarry Smith * - Pipelined depth :math:`\ell` Conjugate Gradient 649*7f296bb3SBarry Smith - ``KSPPIPELCG`` 650*7f296bb3SBarry Smith - --- 651*7f296bb3SBarry Smith - X 652*7f296bb3SBarry Smith - X 653*7f296bb3SBarry Smith * - Pipelined predict-and-recompute Conjugate Gradient 654*7f296bb3SBarry Smith - ``KSPPIPEPRCG`` 655*7f296bb3SBarry Smith - --- 656*7f296bb3SBarry Smith - X 657*7f296bb3SBarry Smith - X 658*7f296bb3SBarry Smith * - Pipelined Conjugate Gradient over iteration pairs 659*7f296bb3SBarry Smith - ``KSPPIPECG2`` 660*7f296bb3SBarry Smith - --- 661*7f296bb3SBarry Smith - X 662*7f296bb3SBarry Smith - X 663*7f296bb3SBarry Smith * - Pipelined flexible Conjugate Gradient 664*7f296bb3SBarry Smith - ``KSPPIPEFCG`` 665*7f296bb3SBarry Smith - --- 666*7f296bb3SBarry Smith - X 667*7f296bb3SBarry Smith - X 668*7f296bb3SBarry Smith * - Pipelined stabilized Bi-Conjugate Gradients 669*7f296bb3SBarry Smith - ``KSPPIPEBCGS`` 670*7f296bb3SBarry Smith - --- 671*7f296bb3SBarry Smith - X 672*7f296bb3SBarry Smith - X 673*7f296bb3SBarry Smith * - Pipelined Conjugate Residual 674*7f296bb3SBarry Smith - ``KSPPIPECR`` 675*7f296bb3SBarry Smith - --- 676*7f296bb3SBarry Smith - X 677*7f296bb3SBarry Smith - X 678*7f296bb3SBarry Smith * - Pipelined flexible GMRES 679*7f296bb3SBarry Smith - ``KSPPIPEFGMRES`` 680*7f296bb3SBarry Smith - --- 681*7f296bb3SBarry Smith - X 682*7f296bb3SBarry Smith - X 683*7f296bb3SBarry Smith * - Pipelined Generalized Conjugate Residual 684*7f296bb3SBarry Smith - ``KSPPIPEGCR`` 685*7f296bb3SBarry Smith - --- 686*7f296bb3SBarry Smith - X 687*7f296bb3SBarry Smith - X 688*7f296bb3SBarry Smith * - Pipelined GMRES 689*7f296bb3SBarry Smith - ``KSPPGMRES`` 690*7f296bb3SBarry Smith - --- 691*7f296bb3SBarry Smith - X 692*7f296bb3SBarry Smith - X 693*7f296bb3SBarry Smith``` 694