Complex Variable Technique in Compact 2-D Order-Marching Time-Domain Method

Abstract

In this paper, we introduce a compact two-dimensional (2-D) complex variable technique with the order-marching time-domain (OMTD) scheme to solve lossy uniform transmission line problems. By applying the complex variable technique to dealing with the partial derivative with respect to wave propagation direction in Maxwell's equations, the spatial attenuation along the propagation direction will be taken into account. Thus, in the heavy loss cases, more accurate results can be obtained as compared with conventional real variable technique. At the same time, the weighted Laguerre polynomials and Galerkin's testing procedure are chosen to treat with the time variable analytically. This OMTD method is free of stability constraint and may be computationally much more efficient than the finite-difference time-domain (FDTD) method with too many time steps to compute the solution. In the numerical example, the proposed method shows its advantage of efficiency and accuracy.