A simple method to determine the time‐step size to achieve a desired dispersion accuracy in ADI‐FDTD

Abstract

AbstractThis paper presents a simple approach to determine the time‐step size required in the alternate‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD) method in order to obtain a desired numerical dispersion accuracy. The Courant number, the desired dispersion accuracy, and the maximum mesh size Δmax = max(Δx, Δy, Δz) are governed by the numerical dispersion relation, which can be solved by a simple root‐finding algorithm to evaluate the Courant number and hence the time‐step size for a given mesh size and accuracy. The time‐step size is independent of the aspect ratio. To determine if ADI‐FDTD is more efficient than the Yee's FDTD, this paper provides a simple relation to evaluate the relative Courant–Friedrich–Levy number (CFLN) from the Courant number and the aspect ratio. The ADI‐FDTD method is more efficient than Yee's FDTD when the aspect ratio is high or the mesh density is very large. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 487–490, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20012