Split-step TLM (SS TLM)-a new scheme for accelerating electromagnetic-field simulation

A new unconditionally stable three-dimensional (3-D) transmisson-line (TLM) algorithm is presented. It is stable regardless of the selected time-step. This new algorithm is based on a split-step theory, whose numerical implementation is given in detail. In addition, the theoretical proof of its unconditional stability is provided. This feature provides some potential advantage for time-domain electromagnetic-field computation as the number of iterations can be arbitrarily reduced for a given space sampling. Unfortunately, it is shown that the numerical dispersion of the new scheme increases when the time-step is different from the maximum value of the standard TLM. However, it is shown that some substantial computer cost reduction can be achieved when irregular meshing is used, as compared to classical 3-D TLM schemes. Thus, a new meshing strategy to improve the scheme accuracy is presented and validated through several examples.

I. Introduction

THE transmission-line matrix (TLM) method is an efficient numerical technique for electromagnetic-field computation [1], [2]. This method is based on a volume discretization of the computational domain and is, hence, well suited for the analysis of arbitrary geometry. As the finite difference time domain (FDTD), the TLM is a time-domain technique that allows wide-band characterization in a single run by applying Fourier transform to time-domain responses. However, the TLM is less dispersive and has the advantage of computing the six-field components at the same location and time. In addition, the TLM is fully compatible with rigorous segmentation techniques [3]. Unfortunately, like FDTD, the TLM is computationally expensive in both CPU time and memory. In particular, this requirement becomes exhaustive when analyzed structures contain fine details. Indeed, in that case, graded mesh is usually used to reduce memory requirement. As a result, the time-step is reduced in proportion to the smallest cell size and, correspondingly, the amount of iterations.