Stability Analysis of Yee Schemes to PML and UPML for Maxwell Equations

Abstract

We utilize Fourier methods to analyze the stability of the Yee difference schemes for Bérenger PML (perfectly matched layer) as well as the UPML (uniaxial perfectly matched layer) systems of two-dimensional Maxwell equations. Using a practical spectrum stability concept, we find that the two schemes are spectrum stable under the same conditions for mesh sizes. Besides, we prove that the UPML schemes with the same damping in both directions are stable. Numerical examples are given to confirm the stability analysis for the PML method.