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 58 articles , 1 standard article )

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  1. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  2. Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices (2016)
  3. Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef: Matrix reordering using multilevel graph coarsening for ILU preconditioning (2015)
  4. Salkuyeh, Davod Khojasteh; Rafiei, Amin; Roohani, Hadi: ILU preconditioning based on the FAPINV algorithm (2015)
  5. Carpentieri, Bruno; Liao, Jia; Sosonkina, Masha: VBARMS: a variable block algebraic recursive multilevel solver for sparse linear systems (2014)
  6. Castillo, P.E.; Sequeira, F.A.: Computational aspects of the local discontinuous Galerkin method on unstructured grids in three dimensions (2013)
  7. Vannieuwenhoven, Nick; Meerbergen, Karl: IMF: an incomplete multifrontal $LU$-factorization for element-structured sparse linear systems (2013)
  8. Ferronato, Massimiliano: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives (2012)
  9. Ferronato, M.; Janna, C.; Pini, G.: Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models (2012)
  10. Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef: Modification and compensation strategies for threshold-based incomplete factorizations (2012)
  11. Wu, Jian Ping; Zhao, Jun; Song, Jun Qiang; Li, Xiao Mei: A parallelization technique based on factor combination and graph partitioning for general incomplete Lu factorization (2012)
  12. Bozdağ, Doruk; Çatalyürek, Ümit V.; Gebremedhin, Assefaw H.; Manne, Fredrik; Boman, Erik G.; Özgüner, Füsun: Distributed-memory parallel algorithms for distance-2 coloring and related problems in derivative computation (2010)
  13. Xiang, Hua; Grigori, Laura: Kronecker product approximation preconditioners for convection-diffusion model problems (2010)
  14. Bozdağ, Doruk; Gebremedhin, Assefaw H.; Manne, Fredrik; Boman, Erik G.; Catalyurek, Umit V.: A framework for scalable greedy coloring on distributed-memory parallel computers (2008)
  15. Bollhöfer, Matthias; Notay, Yvan: JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices (2007)
  16. Maclachlan, Scott; Saad, Yousef: Greedy coarsening strategies for nonsymmetric problems (2007)
  17. Hénon, Pascal; Saad, Yousef: A parallel multistage ILU factorization based on a hierarchical graph decomposition (2006)
  18. Kraus, J.K.: Algebraic multilevel preconditioning of finite element matrices using local Schur complements. (2006)
  19. Shen, Chi; Zhang, Jun: Performance study and analysis of parallel multilevel preconditioners (2006)
  20. Gebremedhin, Assefaw Hadish; Manne, Fredrik; Pothen, Alex: What color is your Jacobian? Graph coloring for computing derivatives (2005)

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