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An adaptive finite element PML method for Helmholtz equations in periodic heterogeneous media

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Abstract

The paper concerns the numerical solution for the wave propagation problem in periodic heterogeneous media. The homogenization method is utilized for the solution in the bounded periodic structure with highly oscillating coefficients. The perfectly matched layer (PML) technique is adopted to truncate the unbounded physical domain into a bounded computational domain, and the exponential convergence of Cartesian PML is generalized to the Helmholtz transmission problem in periodic heterogeneous media. An efficient adaptive finite element algorithm based on reliable a posteriori error estimate is extended to solve the homogenized PML problem, and the reliability of the estimator is established. Numerical experiments are included to demonstrate the competitive behavior of the proposed method.

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Data Availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100190, People’s Republic of China

    Xue Jiang, Zhongjiang Sun & Lijuan Sun

  2. College of Mathematics, Sichuan University, Chengdu, 610065, People’s Republic of China

    Qiang Ma

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  1. Xue Jiang
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  2. Zhongjiang Sun
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  3. Lijuan Sun
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  4. Qiang Ma
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Correspondence to Xue Jiang.

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The research of XJ was supported in part by China NSF Grant 12171017. The research of QM was supported in part by China NSF Grant 11801387.

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Jiang, X., Sun, Z., Sun, L. et al. An adaptive finite element PML method for Helmholtz equations in periodic heterogeneous media. Comp. Appl. Math. 43, 242 (2024). https://doi.org/10.1007/s40314-024-02770-y

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