Development and analysis of an equivalent Drude metamaterial perfectly matched layer model

Abstract

This paper focuses on a perfectly matched layer (PML) model developed by Bécache et al. [6] for Drude metamaterials. Although this PML model performs well in practice — exhibiting stable behavior and effectively absorbing outgoing waves — its stability has not yet been rigorously proven for general damping coefficients. To address this gap, we derive an equivalent PML model from the original formulation and establish its stability under general damping functions. We then develop a finite element scheme to solve the equivalent PML model and provide proofs for both its discrete stability and optimal error estimates. Finally, we present numerical results to support our theoretical analysis and to demonstrate the effectiveness of the equivalent PML model in absorbing outgoing waves.