Comparison of the dispersion properties of several low-dispersion finite-difference time-domain algorithms

A comparison of the accuracy of several low-dispersion finite-difference time-domain (FDTD) schemes in two dimensions is presented. Each algorithm is reviewed and its FDTD update equations presented. The dispersion relation of each FDTD algorithm is also given. The accuracy of each FDTD scheme is compared via direct evaluation of the dispersion relation. Results are presented showing the dispersion errors of each algorithm as a function of propagation angle and cell size. Tables are shown that present for each algorithm the optimal Courant number at a specified discretization as well as the number of floating point operations needed to update each cell (three fields) at each time step. The advantages and disadvantages of each algorithm are briefly discussed. While some schemes are more wideband than others, almost all provide substantial improvement in the dispersion errors compared with the classical Yee FDTD algorithm.