Instable 3D ADI-FDTD open-region simulation

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method has been introduced as an unconditionally stable FDTD algorithm. It was shown through numerous works that the ADI-FDTD algorithm is stable both analytically and numerically even when the Courant-Friedrich-Levy (CFL) limit is exceeded. However, in open-region radiation problems, mesh-truncation techniques or absorbing boundary conditions (ABCs) are needed to terminate the boundary. These truncation techniques represent, in essence, differential operators that are discretized using a distinct differencing scheme. When solving open-region problems, the boundary scheme is expected to affect the stability behavior of the ADI-FDTD simulation regardless of its theoretical imperatives. In our previous work we showed that implementing 3rd order Higdon´s in 2D ADI-FDTD scheme causes instability. In this work, we extend the work to three-dimensional (3D) space and show that the 3D ADI-FDTD method also can be rendered instable when higher-order mesh truncation techniques are used such as Higdon´s operators. This finding shows that the stability of any finite-difference time-domain based scheme cannot be studied independently of the mesh-truncation methods essential for simulation of open-region problems