ction Implicit (ADI) which shows better accuracy may experience lower sta- method [Smit65] has been introduced to the FDTD bility. Some methods such as the perfectly matched layer [Nami99], [ZhCZ00]. The standard explicit FDTD are especially good at gaining accuracy and some methods [Yee66] has to satisfy the CFL bound [Tafl95] to be such as Higdon, Mur 1st and 2nd, and Liao's Absorbing stable. Cases requiring a small spatial discretisation lead Boundary Condition (AbBC) are good at gaining flexi- to excessive time sampling and increase the total Central bility and have simple construction procedures with rel- Processing Unit (CPU) time required for the FDTD. atively small data storage requirements. Liao's AbBC is The maximum At possible in FDTD under the CFL interesting in that it does not have any media parameter condition is defined as AtCFL On the other hand, ADI- such as relative permittivity. This means Liao's AbBC can FDTD is unconditionally stable when taking sampling be easily constructed in the inhomogeneous environ- times At greater than the limit, keeping the total elapsed ment, while other boundary conditions based on one-way time within a practical range. At/AtCFL is called the wave equations such as Mur 1st and Mur 2nd AbBCs Courant-Friedrichs-Lewy Number (CFLN) NCFL. Thus have media parameters. The nature of Liao's AbBC has ADI-FDTD is attractive when, for example, studying the been previously investigated [RaAr95], [ChWa92], influence of skin effects in conductive materials or signal [PrSh97], and [Rama99] concludes that Liao's higher reflections in lossy media for microwave imaging with order AbBC is unstable and even a 2nd order Liao's AbBC UWB systems. These UWB systems typically have fre- exhibits some extent of instability. The higher order quency dependent lossy media parameters but ADI- Liao's AbBC also requires more memory to store the data FDTD and FDTD have media parameters which are for the update of the electromagnetic field values at the constant across frequencies. The adaptation of