A Simple and Accurate Methodology to Optimize Parameter-Dependent Finite-Difference Time-Domain Schemes

A two-stage simple and accurate methodology is presented for the dispersion error minimization of parameter-dependent finite-difference time-domain schemes over a useful bandwidth. The methodology is rigorously developed for both 2-D and 3-D schemes. First, the anisotropy error is treated by expanding the spatial part of the numerical dispersion relation in a cosine-Fourier series, and eliminating the contribution of the angle-dependent terms. The dispersion error is then corrected by employing a modified single-frequency accurate temporal finite-difference operator. This modification can be translated into the parameters of the updating equations, which greatly simplifies its programming. The theoretically derived results are further supported by numerical experiments.