Skip to main content
SpringerLink
Log in

Hybrid Parallel Approach of Splitting-Up Conjugate Gradient Method for Distributed Memory Multicomputers

  • Conference paper
  • First Online:
Book cover Advances in Information and Communication (FICC 2019)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 70))

Included in the following conference series:

  • 1479 Accesses

Abstract

This paper describes several variants of SPCG (Splitting Up Conjugate Gradient) method suitable for parallel computing and evaluates the performance and the speed of convergence on a distributed-memory multicomputer. SP (Splitting-Up) preconditioner can be easily parallelized because other dimensions except for one dimension are independent. Among the variants, one of incomplete SPCG method, which does not carry out one of three tridiagonal matrix solvers, achieves the best performance, and this method is about 20 times faster than one-process version of the SPCG method on 32 CPU cores of the multicomputer.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)

    Article  MathSciNet  Google Scholar 

  2. Wakatani, A.: An incomplete splitting-up conjugate gradient method for parallel computing. Int. J. Comput. Technol. Appl. 7(5), 236–243 (2016)

    Google Scholar 

  3. Osaka University. http://www.hpc.cmc.osaka-u.ac.jp/sx-ace/

  4. Duff, I.S., Meurant, G.A.: The effect of ordering on preconditioned conjugate gradients. BIT Numer. Math. 29(14), 635–657 (1989)

    Article  MathSciNet  Google Scholar 

  5. Odanaka, S., Nogi, T.: Massively parallel computation using a splitting-up operator method for three-dimensional device simulation. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 14(7), 824–832 (1995)

    Article  Google Scholar 

  6. Wakatani, A.: A parallel and scalable algorithm for ADI method with pre-propagation and message vectorization. In: Parallel Computing, vol. 30, pp. 1345–1359 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We are grateful to Professor Tatsuo Nogi of Kyoto University for helpful discussions. I would like to express my gratitude to both professors. Tshis work was supported by JSPS KAKENHI Grant Number 18K02920. This research was also partially supported in part by MEXT, Japan.

Author information

Authors and Affiliations

  1. Faculty of Informatics and Intelligence, Konan University, Kobe, 658-8501, Japan

    Akiyoshi Wakatani

Authors
  1. Akiyoshi Wakatani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Akiyoshi Wakatani .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

  2. The Science and Information (SAI) Organization, Bradford, UK

    Rahul Bhatia

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wakatani, A. (2020). Hybrid Parallel Approach of Splitting-Up Conjugate Gradient Method for Distributed Memory Multicomputers. In: Arai, K., Bhatia, R. (eds) Advances in Information and Communication. FICC 2019. Lecture Notes in Networks and Systems, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-030-12385-7_82

Download citation

Publish with us

Policies and ethics

Search

Navigation