Closed-form expressions for coefficients used in FD-TD high-order boundary conditions

P. A. Tirkas et al. (see IEEE Trans. Antennas Propagat., vol.40, no.10, p.1215-1222, 1992) presented an algorithm for implementing absorbing boundary conditions of arbitrarily high order in finite-difference-time-domain (FD-TD) studies. However, they did not provide explicit formulas for determining the expansion coefficients used in the Pade approximations of the pseudo-differential operator. Instead, the user is required to determine the roots of a polynomial using numerical methods that require computational effort and yield only approximate results. Exact expressions for the desired coefficients that are valid for Pade expansions of any order are presented.<>