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

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.