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

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 $O({\kappa }^{-1})$. We then analyze the first-order Nédélec edge element method and its continuous interior penalty counterpart. Under the condition that ${\kappa }^3{h}^2$ is sufficiently small, the preasymptotic errors in the energy norm and the $\kappa$-scaled ${\mathbf{L}}^2$ norm are of orders $O(\kappa h+{\kappa }^3{h}^2)$ and $O({\kappa }^2{h}^2+{\kappa }^3{h}^2)$, respectively. Numerical experiments confirm the theoretical results.