Analysis and application of a spatial fourth-order finite difference scheme for the Ziolkowski's PML model

Abstract

Perfectly Matched Layer (PML) technique is an effective tool to reduce the unbounded wave propagation problem to a bounded domain problem. In this paper, we develop and analyze a fourth-order in space finite difference scheme for solving the Ziolkowski's PML model. Though fourth-order in space schemes have been widely used in solving Maxwell's equations, few papers provide a rigorous convergence analysis. One of the major contributions here is to fill this gap by proving the fourth-order pointwise convergence of the scheme. Numerical results are presented to justify our analysis, and demonstrate the effectiveness of this PML model in absorbing outgoing waves.