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Convergence analysis of HSS-multigrid methods for second-order nonselfadjoint elliptic problems

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Abstract

In this paper, the multigrid methods using Hermitian/skew-Hermitian splitting (HSS) iteration as smoothers are investigated. These smoothers also include the modified additive and multiplicative smoothers which result from subspace decomposition. Without full elliptic regularity assumption, it is shown that the multigrid methods with these smoothers converge uniformly for second-order nonselfadjoint elliptic boundary value problems if the mesh size of the coarsest grid is sufficiently small (but independent of the number of the multigrid levels). Numerical results are reported to confirm the theoretical analysis.

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Acknowledgements

We would like to thank the referees for their insightful and valuable suggestions, which greatly improved the original manuscript of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, P.R. China

    Shishun Li

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Shishun Li & Zhengda Huang

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  1. Shishun Li
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  2. Zhengda Huang
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Correspondence to Shishun Li.

Additional information

Communicated by Jan Hesthaven.

Supported by the National Natural Science Foundation of China (Grant No. 10731060) and ZPNSFC (Grant No. LY12A01023).

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Li, S., Huang, Z. Convergence analysis of HSS-multigrid methods for second-order nonselfadjoint elliptic problems. Bit Numer Math 53, 987–1012 (2013). https://doi.org/10.1007/s10543-013-0433-5

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  • DOI: https://doi.org/10.1007/s10543-013-0433-5

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