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Performance Analysis of the Chebyshev Basis Conjugate Gradient Method on the K Computer

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Parallel Processing and Applied Mathematics (PPAM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9573))

Abstract

The conjugate gradient (CG) method is useful for solving large and sparse linear systems. It has been pointed out that collective communication needed for calculating inner products becomes serious performance bottleneck when executing the CG method on massively parallel systems. Recently, the Chebyshev basis CG (CBCG) method, a communication avoiding variant of the CG method, has been proposed, and theoretical studies have shown promising results, particularly for upcoming exascale supercomputers. In this paper, we evaluate the CBCG method on an actual system, namely the K computer, to examine the potential of the CBCG method. We first construct a realistic performance model that reflects the computation on the K computer, and the model indicates that the CBCG method is faster than CG method if the number of cores is sufficient large. We then measure the execution time of both methods on the K computer, and obtained results agree with our estimation.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments. This research used the results of the “RIKEN AICS HPC computational science internship program 2014”. This research also used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science(Project ID: ra000005). This work was partially supported by the Japan Society for the Promotion of Science KAKENHI (grant numbers 25330144, 15H02708, and 15K16000).

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Authors and Affiliations

  1. Kogakuin University, Tokyo, Japan

    Yosuke Kumagai, Akihiro Fujii & Teruo Tanaka

  2. RIKEN Advanced Institute for Computational Science, Kobe, Japan

    Yusuke Hirota, Takeshi Fukaya & Toshiyuki Imamura

  3. JST CREST, Tokyo, Japan

    Yusuke Hirota, Takeshi Fukaya & Toshiyuki Imamura

  4. Hokkaido University, Hokkaido, Japan

    Takeshi Fukaya

  5. The University of Tokyo, Tokyo, Japan

    Reiji Suda

Authors
  1. Yosuke Kumagai
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  2. Akihiro Fujii
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  3. Teruo Tanaka
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  4. Yusuke Hirota
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  5. Takeshi Fukaya
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  6. Toshiyuki Imamura
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  7. Reiji Suda
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Corresponding author

Correspondence to Yosuke Kumagai .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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© 2016 Springer International Publishing Switzerland

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Kumagai, Y. et al. (2016). Performance Analysis of the Chebyshev Basis Conjugate Gradient Method on the K Computer. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2015. Lecture Notes in Computer Science(), vol 9573. Springer, Cham. https://doi.org/10.1007/978-3-319-32149-3_8

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  • DOI: https://doi.org/10.1007/978-3-319-32149-3_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32148-6

  • Online ISBN: 978-3-319-32149-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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