On the modeling of conducting media with the unconditionally stable ADI-FDTD method

The Courant-Friedrich-Levy stability condition has prevented the conventional finite-difference time-domain (FDTD) method from being effectively applied to conductive materials because of the fine mesh required for the conducting regions. In this paper, the recently developed unconditionally stable alternating-direction-implicit (ADI) FDTD is employed because of its capability in handling a fine mesh with a relatively large time step. The results show that the unconditionally alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method can be used as an effective universal tool in modeling a medium regardless of its conductivity. In addition, the unsplit perfectly matched layer combined with the ADI-FDTD method is implemented in the cylindrical coordinates and is proven to be very effective even with the cylindrical structures that contain open conducting media.

I. Introduction

Many numerical techniques have been developed to model and simulate RF, microwave, and optical circuits and components. In particular, finite-difference time-domain (FDTD) algorithms have been shown thus far to be the powerful tools to predict RF wave behaviors in various circuit media [1], except for the highly conductive materials. In a highly conductive medium, due to the skin effect, a very fine mesh is required to account for the rapidly changing fields. Such a fine mesh leads to a small cell size, which, in turn, forces the time step to be small because of the Courant–Friedrich–Levy stability (CFL) condition. In a normal circumstance at a microwave frequency, the time step is so small that it makes the number of FDTD iterations very large even for simulation of one cycle of a microwave signal. Consequently, effective schemes need to be developed for modeling of highly conductive materials.