Stability analysis of the Mur´s absorbing boundary condition in the alternating direction implicit finite-difference method

The stability analysis of the Mur´s first order absorbing boundary condition (ABC) in the alternating direction implicit finite-difference time-domain (ADI-FDTD) method is presented. The theoretical stability analysis of this scheme is studied by deriving the amplification matrix. The effect of wave propagation direction on the stability of this scheme is investigated. From the stability analysis, it is found that the Mur´s first order ABC in the ADI-FDTD method will be unstable. The instability of the scheme is validated by means of actual numerical simulations