Mathematical analysis of Ziolkowski’s PML model with application for wave propagation in metamaterials

Abstract

In this paper we investigate one Perfectly Matched Layer (PML) model proposed by Ziolkowski in 1999. Various schemes for solving this PML model have been developed and have been shown to be effective in absorbing outgoing waves when the wave propagation in unbounded domain problem is reduced to a bounded domain problem. However, a rigorous analysis of this model is lacking. In this paper we establish the stability of this PML model and propose a fully-discrete finite element scheme to solve this model with edge elements. Discrete stability and optimal error estimate of this scheme are proved. Numerical results justifying the analysis and demonstrating the effectiveness of this PML model are presented.