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The Flexible ILU Preconditioning for Solving Large Nonsymmetric Linear Systems of Equations

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Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing (EPASA 2015)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 117))

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Abstract

The ILU factorization is one of the most popular preconditioners for the Krylov subspace method, alongside the GMRES. Properties of the preconditioner derived from the ILU factorization are relayed onto the dropping rules. Recently, Zhang et al. (Numer Linear Algebra Appl 19:555–569, 2011) proposed a Flexible incomplete Cholesky (IC) factorization for symmetric linear systems. This paper is a study of the extension of the IC factorization to the nonsymmetric case. The new algorithm is called the Crout version of the flexible ILU factorization, and attempts to reduce the number of nonzero elements in the preconditioner and computation time during the GMRES iterations. Numerical results show that our approach is effective and useful.

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Authors and Affiliations

  1. School of Fundamental Science and Technology, Graduate School of Science and Technology, Keio University, Yokohama, Japan

    Takatoshi Nakamura

  2. Faculty of Science and Technology, Department of Mathematics, Keio University, Yokohama, Japan

    Takashi Nodera

Authors
  1. Takatoshi Nakamura
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  2. Takashi Nodera
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Corresponding author

Correspondence to Takashi Nodera .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Tetsuya Sakurai

  2. Department of Electrical Engineering and Computer Science, Nagoya University, Nagoya, Aichi, Japan

    Shao-Liang Zhang

  3. RIKEN Advanced Institute for Computational Science, Kobe, Hyogo, Japan

    Toshiyuki Imamura

  4. Department of Communication Engineering and Informatics, University of Electro-Communications, Graduate School of Informatics and Engineering, Tokyo, Japan

    Yusaku Yamamoto

  5. Department of Particle Physics, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Yoshinobu Kuramashi

  6. Department of Applied Mathematics and Physics, Tottori University, Tottori, Japan

    Takeo Hoshi

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Nakamura, T., Nodera, T. (2017). The Flexible ILU Preconditioning for Solving Large Nonsymmetric Linear Systems of Equations. In: Sakurai, T., Zhang, SL., Imamura, T., Yamamoto, Y., Kuramashi, Y., Hoshi, T. (eds) Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing. EPASA 2015. Lecture Notes in Computational Science and Engineering, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-62426-6_4

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