Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

TL;DR

This paper introduces a uniaxial PML method for 3D time-domain electromagnetic scattering, proving its stability and exponential convergence, especially advantageous for anisotropic scatterers, with detailed error estimates and analysis.

Contribution

The paper develops and analyzes a uniaxial PML approach for electromagnetic scattering, demonstrating stability and exponential convergence, improving upon previous spherical PML methods.

Findings

Proved well-posedness and stability of the uniaxial PML method.

Established exponential convergence with respect to PML parameters.

Provided error estimates between original and PML solutions.

Abstract

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).