Efficient Abc for the Frequency Dependent Alternating Direction-Implicit FDTD Method

Abstract

Ultra WideBand (UWB) signals have a high potential for a wide range of applications. The Finite-Difference Time-Domain (FDTD) method is widely used in the development of UWB technology but has still two main limitations. One is that material parameters are constant over the whole frequency range. Frequency dependent materials can be accommodated by adopting a Debye model. The other is that the minimum simulation time is bound by the Courant-Friedrichs-Lewy (CFL) condition, which can be solved by the application of the Alternating Direction-Implicit (ADI) scheme. The combination of Debye model and ADI scheme in FDTD results in the Frequency-Dependent (FD) ADI-FDTD method. This paper proposes an adaptation of the most effective Absorbing Boundary Condition (ABC), the Complex Frequency-Shift (CFS) Perfectly Matched Layer (PML), to FD-ADI-FDTD. The formulation of CFS-PML for FD-ADI-FDTD is proposed and its performance is assessed. The influence of the Courant Number (CFLN), the media parameters and the number of layers are investigated. CFS-PML is tightly integrated into the computation update, so that FD-ADI-FDTD must be rewritten to take it into account. With E the electric field, H the magnetic field, D the electric flux density, the permittivity, µ the permeability and ρ the charge density, Maxwell's equations are written as: