Numerical stability analysis for perfectly matched absorbers

Berenger [1994] developed an artificial absorber for the finite difference time domain (FDTD) method with added degrees of freedom which allowed the absorber interface to be reflectionless to plane waves at all angles of incidence. Very few studies have been performed on time domain stability analysis in the electromagnetics community. To date there has been no literature published on the stability analysis of Berenger´s equations. This paper studies the numeric stability of a time domain implementation of Berenger´s equations. Here the Von Neumann analysis [Strikwerda et al. 1989] is used and a characteristic polynomial is developed. Conditions under which all roots of this polynomial are bounded by one imply numeric stability.