The influence of the time step on the numerical dispersion error of an unconditionally stable 3‐D ADI‐FDTD method: A simple and unified approach to determine the maximum allowable time step required by a desired numerical dispersion accuracy

Abstract

AbstractIn this paper, by analyzing the numerical dispersion property of an unconditionally stable three‐dimensional alternating direction implicit finite‐difference time‐domain (ADI‐FDTD) method, the influence of the time steps on the numerical dispersion error of the method is investigated. It is demonstrated that, to keep the numerical dispersion error of the method within a certain level of accuracy, an upper limit for the time step allowed to be used in the method exists and it can be theoretically determined. Particularly, in order to systematically determine the upper limit for the computational domain meshed with arbitrary uniform and non‐uniform grids, a special strategy used to divide Yee's cells into different categories is developed. Subsequently, a simple and unified approach for determining the maximum allowable time steps (i.e., the upper limits) from a desired numerical dispersion accuracy is proposed. Most importantly, with the help of the proposed approach, the maximum allowable time steps can be simply and easily determined once the meshing of structures (meshed with either uniform or non‐uniform grids) is known, i.e., without carrying out any real ADI‐FDTD simulations for the structures. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 60–65, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10516