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arXiv · 2610.19982

Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number

Jian Shi·Yonglin Li·Haijun Wu
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Abstract

We study a spherical perfectly matched layer (PML) method for the time-harmonic Maxwell scattering problem with large wavenumber. Using vector spherical harmonics and a modal transformation for the coupled transverse magnetic components, we establish the sharp wavenumber-explicit stability estimate for the truncated PML problem and prove that its inf-sup constant is of order $O(κ^{-1})$. We then analyze the first-order Nédélec edge element method and its continuous interior penalty counterpart. Under the condition that $κ^3h^2$ is sufficiently small, the preasymptotic errors in the energy norm and the $κ$-scaled $\mathbf{L}^2$ norm are of orders $O(κh+κ^3h^2)$ and $O(κ^2h^2+κ^3h^2)$, respectively. Numerical experiments confirm the theoretical results.

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Jian Shi, Yonglin Li, Haijun Wu. 2026-10-14. Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number. https://arxiv.org/abs/2610.19982

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