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

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. •The very few papers devoted to convergence analysis for 4th-order spatial FDTD scheme for PML model.•No rigorous error estimate has been proved for 4th-order FDTD scheme, to our best knowledge.•The proof of stability analysis and convergence estimate are original.•Numerical results demonstrate the effectiveness of this PML in absorbing outgoing waves.