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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. Index Terms--Alternating-direction-implicit-finite-difference time-domain (ADI-FDTD) method, highly conductive materials, perfectly matched layer (PML).

An unconditionally stable finite-difference time-domain (FDTD) method in the cylindrical coordinate system is presented in this paper. In it, the alternating-direction-implicit (ADI) method is applied, leading to a cylindrical ADI-FDTD scheme where the time step is no longer restricted by the stability condition, but by the modeling accuracy. In difference from the conventional ADI method, in which the alteration is applied in each coordinate direction, the ADI scheme here performs alternations in the mixed coordinates so that only two alternations in solution marching are required at each time step in the three-dimensional formulation. In difference from its counterpart in the Cartesian coordinate system, the cylindrical ADI-FDTD includes an additional special treatment along the vertical axis of the cylindrical coordinates to overcome singularity. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness of the cylindrical algorithm in solving electromagnetic-field problems. Index Terms--Alternating-direction-implicit (ADI) method, cylindrical coordinate system, finite-difference time-domain (FDTD) method, unconditional stability.