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A parallel version of GPBi-CG method suitable for distributed parallel computing

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Abstract

In this paper, one new parallel version of GPBi-CG method (PGPBi-CG method, in brief) is proposed for solving large sparse linear systems with unsymmetrical coefficient matrices on distributed parallel environments. The method reduces three global synchronization points to one by reconstructing GPBi-CG method and the communication time required for the inner product can be efficiently overlapped with computation time of vector updates. It combines the elements of numerical stability with the characteristics of design of parallel algorithms. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the PGPBi-CG method has better parallelism and scalability than the GPBi-CG method. Numerical experiments show that the scalability can be improved by a factor 3 and the improvement in parallel communication performance approaches 66.7 %.

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Acknowledgments

The authors would like to thank the referees and Editor for their helpful and detailed suggestions for revising this manuscript.

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Authors and Affiliations

  1. Institute of Data and Knowledge Engineering, School of Computer and Information Engineering, Henan University, Kaifeng, Henan, 475004, People’s Republic of China

    Xian-Yu Zuo, Feng-Bin Zheng & Ning Li

  2. Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou, Henan, 450015, People’s Republic of China

    Li-Tao Zhang

  3. Laboratory of Computationary Physics, Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing, 100088, People’s Republic of China

    Tong-Xiang Gu

Authors
  1. Xian-Yu Zuo
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  2. Li-Tao Zhang
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  3. Tong-Xiang Gu
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  4. Feng-Bin Zheng
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  5. Ning Li
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Corresponding authors

Correspondence to Xian-Yu Zuo or Feng-Bin Zheng.

Additional information

Communicated by Philippe Devloo.

This research of this author is supported by the NSFC (61202098, 61203179, 61170309, 11171039, 11471098 and 61272544), China Postdoctoral Science Foundation (2014M552001), Henan Province Postdoctoral Science Foundation (2013031), Aeronautical Science Foundation of China (2013ZD55006), Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (2013GGJS-142), Major Project of development foundation of science and technology of CAEP (2012A0202008).

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Zuo, XY., Zhang, LT., Gu, TX. et al. A parallel version of GPBi-CG method suitable for distributed parallel computing. Comp. Appl. Math. 35, 579–593 (2016). https://doi.org/10.1007/s40314-014-0206-z

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  • DOI: https://doi.org/10.1007/s40314-014-0206-z

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