Stability and dispersion analysis for higher order 3-D ADI-FDTD method

In this paper, the stability and dispersion analysis for higher order three-dimensional (3-D) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) methods is presented. Starting with the stability and dispersion analysis of the fourth order 3-D ADI-FDTD method, which adopts the fourth order cell-centered finite difference scheme for the spatial differential operator, we generalize the analysis to other higher order methods based on the sixth and tenth order cell-centered finite difference schemes. To the best of our knowledge, this is the first time that a comprehensive study of the stability and dispersion characteristics for one series of higher order 3-D ADI-FDTD methods is presented. Our analysis results show that all the higher order ADI-FDTD methods that are based on cell-centered finite difference schemes are unconditionally stable. The generalized form of the dispersion relations for these unconditionally stable ADI-FDTD methods is also presented. Using the relations attained, the effects of the order of schemes, mesh size and time step on the dispersion are illustrated through numerical results. This study will be useful for the selection and evaluation of various higher order ADI methods.