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

## TL;DR

This paper presents a convergence analysis of the PML method for 3D time-domain electromagnetic scattering, establishing its exponential convergence and well-posedness using Laplace transform and energy methods.

## Contribution

It provides the first convergence proof for the time-domain PML method applied to 3D Maxwell equations, including stability and exponential decay estimates.

## Key findings

- Proves well-posedness and stability of the PML problem.
- Establishes exponential convergence of the PML method.
- First convergence result for 3D time-domain Maxwell PML.

## Abstract

In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coordinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Green's function for the Maxwell equations in the free space.