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Local and Parallel Finite Element Algorithms for the Transmission Eigenvalue Problem

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Abstract

Based on the work of Xu and Zhou (Math Comp 69:881–909, 2000), we establish local and parallel algorithms for the Helmholtz transmission eigenvalue problem. For the \(H^2\)-conforming finite element and the spectral element approximations, we prove the local error estimates and the efficiency of local and parallel algorithms. Numerical experiments indicate that our algorithms are easy to implement on the existing packages, and can be used to solve the transmission eigenvalue problem with local low smooth eigenfunctions efficiently.

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Hai Bi, Jiayu Han & Yidu Yang

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  1. Hai Bi
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  2. Jiayu Han
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  3. Yidu Yang
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Correspondence to Yidu Yang.

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Project supported by the National Natural Science Foundation of China (Grant Nos. 11761022, 11561014).

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Bi, H., Han, J. & Yang, Y. Local and Parallel Finite Element Algorithms for the Transmission Eigenvalue Problem. J Sci Comput 78, 351–375 (2019). https://doi.org/10.1007/s10915-018-0770-2

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