Two special notes on the implementation of the unconditionally stable ADI-FDTD method

In this article two special considerations or notes on the implementation of the alternating direction implicit finite-difference-time-domain (ADI-FDTD) method are discussed. In particular, the two notes are (a) the mathematical algorithm used to solve the tridiagonal matrix equation, and (b) the way to apply the excitation. First, it is found that the ADI-FDTD method is not always stable if the algorithm (for solving the tridiagonal matrix equation) proposed in the book Numerical Recipes in C is adopted. Consequently, a simple, efficient, and stable mathematical algorithm for solving the tridiagonal matrix equation of the ADI-FDTD method is presented. Second, it is demonstrated that, to obtain more accurate results for all the field components, the excitation function should be applied to both the first subiteration and the second subiteration, rather than forced in the first subiteration only. The theory proposed in this article is validated through numerical examples. (C) 2002 Wiley Periodicals, Inc.