Relative accuracy of several low-dispersion finite-difference time-domain schemes

For electrically large problems, the numerical dispersion inherent in the classical Yee finite-difference time-domain (FDTD) algorithm can introduce significant errors. Over the past ten years there have been several FDTD schemes published with the goal of reducing dispersion errors. In this paper, a comparison of the 2-D dispersion error of several of these low-dispersion schemes is made. The accuracy of each FDTD scheme is compared via direct evaluation of the dispersion relation governing the algorithm. In addition, numerical experiments were performed to verify the derived dispersion relations. The algorithms compared include Krumpholz and Katehi's MRTD scheme (1996), Hadi and Piket-May's M24 scheme (1997), Cole's Non-Standard scheme (1997), Forgy's isotropic scheme (1998), Nehrbass, Jetvic and Lee's (NJL) reduced dispersion scheme (1998), and Turkel's Ty(2,4) implicit scheme (1998). The dispersion characteristics are typically derived by assuming a time harmonic plane-wave solution in an isotropic, homogeneous, linear and lossless medium.