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An error-resilient redundant subspace correction method

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Computing and Visualization in Science

Abstract

Due to increasing complexity of supercomputers, hard and soft errors are causing more and more problems in high-performance scientific and engineering computation. In order to improve reliability (increase the mean time to failure) of computing systems, a lot of efforts have been devoted to developing techniques to forecast, prevent, and recover from errors at different levels, including architecture, application, and algorithm. In this paper, we focus on algorithmic error resilient iterative solvers and introduce a redundant subspace correction method. Using a general framework of redundant subspace corrections, we construct iterative methods, which have the following properties: (1) maintain convergence when error occurs assuming it is detectable; (2) introduce low computational overhead when no error occurs; (3) require only small amount of point-to-point communication compared to traditional methods and maintain good load balance; (4) improve the mean time to failure. Preliminary numerical experiments demonstrate the efficiency and effectiveness of the new subspace correction method. For simplicity, the main ideas of the proposed framework were demonstrated using the Schwarz methods without a coarse space, which do not scale well in practice.

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Notes

  1. The y-axis is processing units and the x-axis is time. The solid bars stand for computational work and springs stand for inter-process communication.

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Acknowledgements

Cui and Zhang are partially supported by National Key Research and Development Program 2016YFB0201304, by China NSF Grants 91430215 and 91530323, and by National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS). Xu is partially supported by NSF DMS-0915153 and DOE DE-SC0006903.

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Authors and Affiliations

  1. State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Tao Cui & Chen-Song Zhang

  2. Department of Mathematics, Pennsylvania State University, University Park, PA, USA

    Jinchao Xu

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  1. Tao Cui
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  2. Jinchao Xu
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Correspondence to Tao Cui.

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Communicated by Gabriel Wittum.

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Cui, T., Xu, J. & Zhang, CS. An error-resilient redundant subspace correction method. Comput. Visual Sci. 18, 65–77 (2017). https://doi.org/10.1007/s00791-016-0270-6

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