Skip to main content
SpringerLink
Log in

Ainv and bilum preconditioning techniques

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditoner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Saad Y.Iterative Methods for Sparse Linear Systems [M]. New York: PWS Publishing, 1996.

    Google Scholar 

  2. Golub G H, van der Vorst H A. Closer to the solution: iterative linear solver [A]. In: Duff I S, Watson G A Eds.The State of the Art in Numerical Analysis [C]. Oxford: Clarendon Press, 1997, 63–92.

    Google Scholar 

  3. Saad Y, ZHANG Jun. BILUM: block versions of multi-elimination and multi-level ILU preconditioner for general sparse linear systems [J].SIAM J Sci Comput, 1999,20 (6): 2103–2121.

    Article  MATH  MathSciNet  Google Scholar 

  4. Benzi M, Tuma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems [J].SIAM J Sci Comput, 1998,19 (3): 968–994.

    Article  MATH  MathSciNet  Google Scholar 

  5. Chan T F, TANG Wei-pai, Wan W L. Wavelet sparse approximate inverse preconditioners [J].BIT, 1997,37 (3): 644–660.

    MATH  MathSciNet  Google Scholar 

  6. Chow E, Saad Y. Approximate inverse techniques for block-partitioned matrices [J].SIAM J Sci Comput, 1997,18 (6): 1657–1675.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chow E, Saad Y. Approximate inverse preconditioner via sparse-sparse iterations [J].SIAM J Sci Comput, 1998,19 (3): 995–1023.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gould N I M, Scott J A. Sparse approximate-inverse preconditioners using norm minimization techniques [J].SIAM J Sci Comput, 1998,19 (2): 605–625.

    Article  MATH  MathSciNet  Google Scholar 

  9. Grote M, Huckle T. Parallel preconditioning with sparse approximate inverses [J].SIAM J Sci Comput, 1997,18 (3): 838–853.

    Article  MATH  MathSciNet  Google Scholar 

  10. Saad Y. ILUT: a dual threshold incomplete ILU preconditioner [J].Numer Linear Algebra Appl, 1994,1 (4): 387–402.

    Article  MATH  MathSciNet  Google Scholar 

  11. TANG Wei-pai, Wan W L. Sparse approximate inverse smoother for multigrid [J].SIAM J Matrix Anal Appl, 2000,21 (4): 1236–1252.

    Article  MathSciNet  Google Scholar 

  12. Saad Y, ZHANG Jun. Enhanced multi-level block ILU preconditioning strategies for general linear systems [J].J Comput Appl Math, 2001,130 (1/2): 99–118.

    Article  MATH  MathSciNet  Google Scholar 

  13. ZHANG Jun. Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices [J].Appl Numer Math, 2000,35 (1): 67–86.

    Article  MathSciNet  Google Scholar 

  14. Benzi M, Tuma M. A comparative study of sparse approximate inverse preconditioners [J].Appl Numer Math, 1999,30 (2/3): 305–340.

    Article  MATH  MathSciNet  Google Scholar 

  15. Benzi M, Meyer C D, Tuma M. A sparse approximate inverse preconditioner for the conjugate gradient method [J].SIAM J Sci Comput, 1996,17 (5): 1135–1149.

    Article  MATH  MathSciNet  Google Scholar 

  16. Benzi M, Cullum J K, Tuma M. Robust approximate inverse preconditioning for the conjugate gradient method [J].SIAM J Sci Comput, 2000,22 (4): 1318–1332.

    Article  MATH  MathSciNet  Google Scholar 

  17. Benzi M, Tuma M. Orderings for factorized sparse approximate inverse preconditioners [J].SIAM J Sci Comput, 2000,21 (5): 1851–1868.

    Article  MATH  MathSciNet  Google Scholar 

  18. Kolotina L Y, Yeremin A Y. Factorized sparse approximate inverse preconditioning I: theory [J].SIAM J Matrix Anal Appl, 1993,14 (1): 45–58.

    Article  MathSciNet  Google Scholar 

  19. Saad Y. ILUM: a multi-elimination ILU preconditioner for general sparse matrices [J].SIAM J Sci Comput, 1996,17 (4): 830–847.

    Article  MATH  MathSciNet  Google Scholar 

  20. Saad Y, Sosonkina M, ZHANG Jun. Domain decomposition and multi-level type techniques for general sparse linear systems [A]. In: Mandel J, Farhat C, Cai X C Eds.Domain Decomposition Methods 10 [C]. number 218 in Contemporary Mathematics, Providence, RI, AMS, 1998, 174–190.

    Google Scholar 

  21. Saad Y. A flexible inner-outer preconditioned GMRES algorithm [J].SIAM J Sci Comput, 1993,14 (2): 461–469.

    Article  MATH  MathSciNet  Google Scholar 

  22. Saad Y, ZHANG Jun. BILUTM: a domain-based multi-level block ILUT preconditioner for general linear systems [J].SIAM J Matrix Anal Appl, 1999,21 (1): 279–299.

    Article  MATH  MathSciNet  Google Scholar 

  23. ZHANG Jun. On convergence of iterative methods with a fourth-order compact scheme [J].Appl Math Lett, 1997,10 (2): 49–55.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, 100088, Beijing, P. R. China

    Gu Tong-xiang Associate Professor, Doctor & Liu Xing-ping

  2. Supercomputing Center of Computer Network Information Center, Chinese Academy of Science, P. O. Box 349, 100080, Beijing, P. R. China

    Gu Tong-xiang Associate Professor, Doctor & Chi Xue-bin

Authors
  1. Gu Tong-xiang Associate Professor, Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chi Xue-bin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liu Xing-ping
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by WU Qi-guang, Original Member of Editorial Committee, AMM

Foundation items: the National Natural Science Foundation of China (60373015); the State Hi-Tech Research and Development Program of China (2001AA111043); the Foundation of State Key Laboratory of Computational Physics

Biography: GU Tong-xiang (1964≈)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tong-xiang, G., Xue-bin, C. & Xing-ping, L. Ainv and bilum preconditioning techniques. Appl Math Mech 25, 1012–1021 (2004). https://doi.org/10.1007/BF02438350

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02438350

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation