Improved PML formulation for the unconditionally stable D-H ADI-FDTD method

In a large number of electromagnetic problems, the spatial discretization is dominated by very fine geometric details rather than the smallest wavelength of interest. These fine details dictate a small time-step due to the Courant-Friedrichs-Lewy stability bound when an explicit finite-difference time-domain (FDTD) scheme is used, which in turn leads to a large number of computational steps. The use of the alternating direction implicit (ADI) method was introduced for the time-domain analysis of electromagnetic problems to eliminate the Courant stability bound of the explicit FDTD method. We present an improved anisotropic PML (perfectly matched layer) for the unconditionally stable D-H ADI-FDTD method. The relative reflection error observed from numerical experiments is reduced by 15 to 20 dB as compared to the formulation of G. Lazzi (see IEEE Microwave Wireless Comp. Lett., vol.11, no.4, 2001). The error is bound in late time, even for time step lengths that are larger than the Courant stability limit, which implies that the method is unconditionally stable for late time.