Four unequal substep FDTD (4 USS‐FDTD) method with extremely low numerical dispersion error

Abstract

A new unconditionally stable split-step FDTD method is introduced which has unequal substeps. The ratio of the unequal substeps, τ, is utilized to obtain extremely low anisotropic errors. It is shown that for any set of space step and time step values, there is a τ value which gives zero anisotropic error. Polynomials are obtained in terms of time and space step sizes for τ and the average normalized numerical phase velocity which can be used to correct for anisotropic error and the average numerical phase velocity. The 2 polynomials can be integrated into the simulation programs, so that the user gets an almost unity normalized phase velocity in all directions, for any chosen time step size and space step size. In this way, large time steps up to Nyquist rate can be used.The method is also suitable for multidomain applications, which makes the method very efficient. A further study shows that the method is very wideband, and for 1% dispersion, error bandwidth is larger than 10:1. KEYWORDS alternating direction implicit finite difference time domain (ADI-FDTD), LOD-FDTD, numerical dispersion, split-step FDTD