Stability and dispersion analysis of ADI-MRTD and ADI high-order schemes

摘要

The maximum time-step size of the alternating-direction implicit finite-differenc̀e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.