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A Multilevel Correction Method for Interior Transmission Eigenvalue Problem

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Abstract

In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction method can transform the transmission eigenvalue solving in the finest finite element space to a sequence of linear problems and some transmission eigenvalue solving in a very low dimensional spaces. Since the main computational work is to solve the sequence of linear problems, the multilevel correction method improves the overfull efficiency of the transmission eigenvalue solving. Some numerical examples are provided to validate the theoretical results and the efficiency of the proposed numerical scheme.

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Acknowledgements

The work of Hehu Xie is supported in part by the National Natural Science Foundations of China (NSFC 91330202, 11371026, 11001259, 11031006, 2011CB309703), Science Challenge Project (No. JCKY2016212A502), the National Center for Mathematics and Interdisciplinary Science, CAS. The work of Xinming Wu is supported in part by the National Natural Science Foundations of China (NSFC 91330202, 11301089).

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Authors and Affiliations

  1. LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Hehu Xie

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Hehu Xie

  3. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Xinming Wu

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  1. Hehu Xie
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  2. Xinming Wu
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Correspondence to Xinming Wu.

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Xie, H., Wu, X. A Multilevel Correction Method for Interior Transmission Eigenvalue Problem. J Sci Comput 72, 586–604 (2017). https://doi.org/10.1007/s10915-017-0367-1

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  • DOI: https://doi.org/10.1007/s10915-017-0367-1

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