## BILUM

swMATH ID: | 4015 |

Software Authors: | Saad, Yousef; Zhang, Jun |

Description: | BILUM is a set of programs designed for solving general sparse linear systems by using Krylov subspace methods preconditioned by some multi-level block ILU (BILUM) preconditioning techniques. BILUM combines the benefits of generality and robustness of ILU preconditioning techniques with those of grid-independent convergence of multigrid methods. The multi-level algorithms implemented by BILUM are based on the block independent set ordering and multi-elimination techniques. At each level, a block independent set is found by some greedy algorithms such that each block is decoupled with other blocks in the independent set. There is an inherited parallelism associated with this technique. The coefficient matrix is then re-ordered according to the independent set ordering and an approximate block ILU factorization is performed with a reduced system of smaller size. The multi-level structure is constructed by recursively applying the above idea to the approximate Schur complement (the reduced system) until the last reduced system is small enough to be solved by a direct method or a preconditioned iterative method. |

Homepage: | http://www.cs.uky.edu/~jzhang/bilum.html |

Related Software: | ILUM; BILUTM; ILUT; SparseMatrix; ARMS; symrcm; LAPACK; pARMS; BPKit; Wesseling; BFSAI-IC; ITSOL; CGS; ILUS; BoomerAMG; Aztec; AztecOO; P-SPARSLIB; STRUMPACK; Albany/FELIX |

Cited in: | 50 Publications |

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### Cited by 65 Authors

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### Cited in 22 Serials

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