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On the convergence rate of a parallel nonoverlapping domain decomposition method

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Abstract

In recent years, a nonoverlapping domain decomposition iterative procedure, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed. It is known that the convergence rate of this method is 1 − O(h), where h is mesh size. In this paper, the convergence rate is improved to be 1 − O(h 1/2H−1/2) sometime by choosing suitable parameter, where H is the subdomain size. Counter examples are constructed to show that our convergence estimates are sharp, which means that the convergence rate cannot be better than 1 − O(h 1/2H−1/2) in a certain case no matter how parameter is chosen.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Beijing, 100190, China

    Qin LiZhen, Shi ZhongCi & Xu XueJun

Authors
  1. Qin LiZhen
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  2. Shi ZhongCi
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  3. Xu XueJun
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Corresponding author

Correspondence to Xu XueJun.

Additional information

This work was supported by the National Basic Research Program of China (Grant No. 2005CB321701) and the National Natural Science Foundation of China (Grant No. 10731060)

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LiZhen, Q., ZhongCi, S. & XueJun, X. On the convergence rate of a parallel nonoverlapping domain decomposition method. Sci. China Ser. A-Math. 51, 1461–1478 (2008). https://doi.org/10.1007/s11425-008-0103-2

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  • DOI: https://doi.org/10.1007/s11425-008-0103-2

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