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The time-harmonic electromagnetic wave scattering by a bi-periodic elastic body
  • Tielei Zhu,
  • Changkun Wei,
  • Jiaqing Yang
Tielei Zhu
School of Mathematics and Statistics Xi’an Jiaotong University Xi’an Shaanxi 710049 China
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Changkun Wei
School of Mathematics and Statistics Beijing Jiaotong University Beijing 100044

Corresponding Author:ckwei@bjtu.edu.cn

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Jiaqing Yang
School of Mathematics and Statistics Xi’an Jiaotong University Xi’an Shaanxi 710049
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Abstract

This paper concentrates on an interaction scattering problem between the time-harmonic electromagnetic waves and an unbounded periodic elastic medium. The uniqueness results of the interaction problem are established for small frequencies or all frequencies except a discrete set in both the absorbing and non-absorbing medium, and then the existence of solutions is derived by the classical Fredholm alternative. The perfectly matched layer (PML) method is proposed to truncate the unbounded scattering domain to a bounded computational domain. We prove the well-posedness of the solution for the truncated PML problem, where a homogeneous boundary condition is imposed on the outer boundary of the PML. The exponential convergence of the PML method is established in terms of the thickness and parameters of the PML. The proof is based on the PML extension and the exponential decay properties of the modified fundamental solution.
26 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
26 Sep 2022Submission Checks Completed
26 Sep 2022Assigned to Editor
13 Oct 2022Reviewer(s) Assigned
18 Oct 2023Review(s) Completed, Editorial Evaluation Pending
18 Oct 2023Editorial Decision: Revise Minor
27 Oct 20231st Revision Received
30 Oct 2023Submission Checks Completed
30 Oct 2023Assigned to Editor
30 Oct 2023Review(s) Completed, Editorial Evaluation Pending
31 Oct 2023Reviewer(s) Assigned