ILUM

ILUM: A multi-elimination ILU preconditioner for general sparse matrices Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism, in general. A few of the alternatives advocated so far consist of either using some form of polynomial precoditioning or applying the usual ILU factorization to a matrix obtained from a multicolor ordering.par We present an incomplete factorization technique based on independent set orderings and multicoloring. We note that in order to improve robustness, it is necessary to allow the preconditioner to have an arbitrary high accuracy, as is done with ILUs based on threshold techniques. The ILUM factorization described in this paper is in this category. It can be viewed as a multifrontal version of a Gaussian elimination procedure with threshold dropping which has a high degree of potential parallelism.par The emphasis is on methods that deal specifically with general unstructured sparse matrices such as those arising from finite element methods on unstructured meshes.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 64 articles , 1 standard article )

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  1. Bollhöfer, Matthias; Notay, Yvan: JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices (2007)
  2. Maclachlan, Scott; Saad, Yousef: Greedy coarsening strategies for nonsymmetric problems (2007)
  3. Hénon, Pascal; Saad, Yousef: A parallel multistage ILU factorization based on a hierarchical graph decomposition (2006)
  4. Kraus, J. K.: Algebraic multilevel preconditioning of finite element matrices using local Schur complements. (2006)
  5. Shen, Chi; Zhang, Jun: Performance study and analysis of parallel multilevel preconditioners (2006)
  6. Gebremedhin, Assefaw Hadish; Manne, Fredrik; Pothen, Alex: What color is your Jacobian? Graph coloring for computing derivatives (2005)
  7. Guessous, N.; Souhar, O.: The effect of block red-black ordering on block ILU preconditioner for sparse matrices (2005)
  8. Notay, Y.: Algebraic multigrid and algebraic multilevel methods: a theoretical comparison. (2005)
  9. Saad, Yousef: Multilevel ILU with reorderings for diagonal dominance (2005)
  10. Salkuyeh, D. Khojasteh; Toutounian, F.: A block version algorithm to approximate inverse factors (2005)
  11. Shen, Chi; Zhang, Jun; Wang, Kai: Distributed block independent set algorithms and parallel multilevel ILU preconditioners (2005)
  12. Shi, Yuying; Chang, Qianshun: Remark on convergence of algebraic multigrid in the form of matrix decomposition (2005)
  13. Guessous, N.; Souhar, O.: Recursive two-level ILU preconditioner for nonsymmetric M-matrices (2004)
  14. Gu, Tongxiang; Chi, Xuebin; Liu, Xingping: AINV and BILUM preconditioning techniques (2004)
  15. Heath, L. S.; Ribbens, C. J.; Pemmaraju, S. V.: Processor-efficient sparse matrix-vector multiplication (2004)
  16. Saad, Yousef; Soulaimani, Azzeddine; Touihri, Ridha: Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems (2004)
  17. Chow, Edmond; Vassilevski, Panayot S.: Multilevel block factorizations in generalized hierarchical bases. (2003)
  18. Li, Zhongze; Saad, Yousef; Sosonkina, Masha: pARMS: a parallel version of the algebraic recursive multilevel solver. (2003)
  19. Sleijpen, Gerard L. G.; Wubs, Fred W.: Exploiting multilevel preconditioning techniques in eigenvalue computations (2003)
  20. Benzi, Michele: Preconditioning techniques for large linear systems: A survey (2002)