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.

References in zbMATH (referenced in 47 articles )

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  1. Ge, Lixin; Zhang, Jun: Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients (2002)
  2. Saad, Y.; Suchomel, B.: ARMS: an algebraic recursive multilevel solver for general sparse linear systems. (2002)
  3. Shen, Chi; Zhang, Jun: Parallel two level block ILU preconditioning techniques for solving large sparse linear systems (2002)
  4. Wang, Kai; Zhang, Jun: Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning (2002)
  5. Zhang, Jun: A sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices (2002)
  6. Bridson, Robert; Tang, Wei-Pai: Multiresolution approximate inverse preconditioners (2001)
  7. Saad, Yousef; Zhang, Jun: Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems (2001)
  8. Zhang, Jun: A class of multilevel recursive incomplete LU preconditioning techniques (2001)
  9. Zhang, Jun: A grid-based multilevel incomplete LU factorization preconditioning technique for general sparse matrices (2001)
  10. Zhang, Jun: A multilevel dual reordering strategy for robust incomplete LU factorization of indefinite matrices (2001)
  11. Zhang, Jun; Zhao, Jennifer J.: Unconditionally stable finite difference scheme and iterative solution fo 2D microscale heat transport equation (2001)
  12. Benzi, Michele; Haws, John C.; Tuma, Miroslav: Preconditioning highly indefinite and nonsymmetric matrices (2000)
  13. Ge, Lixin; Zhang, Jun: Accuracy, robustness, and efficiency comparison in iterative computation of convection diffusion equation with boundary layers (2000)
  14. Grosz, Lutz: On residual smoothing in ILUM-type preconditioning (2000)
  15. Gupta, Murli M.; Zhang, Jun: High accuracy multigrid solution of the 3D convection-diffusion equation (2000)
  16. Reusken, Arnold: An algebraic multilevel preconditioner for symmetric positive definite and indefinite problems (2000)
  17. Wagner, C.: On the algebraic construction of multilevel transfer operators (2000)
  18. Zhang, Jun: Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices (2000)
  19. Zhang, Jun: Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications (2000)
  20. Zhang, Jun: Preconditioned iterative methods and finite difference schemes for convection-diffusion (2000)