Instable 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 (ABC) 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 this work, we show that the ADI-FDTD method can be rendered unstable when higher-order mesh truncation techniques are used such as Higdon's operators.