Digital spectral domain analysis of the errors in one-dimensional Yee/semi-discrete and Yee/ADI hybrid griddings

The semi-discrete (SD) scheme [1] and the alternate-direction-implicit (ADI) FDTD [2] method have been proven unconditional stable, but less efficient and accurate than the Yee-FDTD method [3]. Since SD and ADI in general are to be used for problems with fine structures, it is natural to increase the efficiency by hybridizing the SD or ADI scheme for the fine structure with the explicit (Yee) FDTD method for the free space region or large structures. This paper is thus to investigate the performance of such a hybrid gridding by deriving analytic expressions for 1-D reflection from and transmission through an SD or ADI mesh embedded in an infinite Yee-FDTD grid in free space. We find that expressions of the same form are applicable to both cases. Numerical results reveal that the hybrid Yee/SD gridding is with less error than the hybrid Yee/ADI gridding.