Application of the locally implicit FVTD method for a substrate integrated waveguide

In this paper, we describe the locally implicit finite volume time domain (LI-FVTD) method for the simulation of a substrate integrated waveguide. A two-dimensional explicit FVTD method suffers from a time step size limitation depending on the ratio between the area of a surface element and its edge lengths. Consequently, the time step size becomes small in the case that there exist objects which are small compared with the wavelength of a propagating wave. We overcome this problem by combing the explicit scheme with a numerically stable implicit scheme and can alleviate the restriction on the time step size. As a result, the proposed method enables the faster simulation than the conventional one by using a larger time step size.