Stability analysis of the PML scheme for CN-FDTD and ADI-FDTD

The alternating direction implicit-finite-difference time-domain (ADI-FDTD) method can be seen as a second-order perturbation of the Crank-Nicolson FDTD (CN-FDTD) scheme. When the PML is introduced for the ADI-FDTD method, the perturbation term will affect the stability of the ADI-FDTD method. In this work, the stability analysis of the PML schemes for the ADI-FDTD and CN-FDTD are demonstrated. It is found that the PML equations for ADI-FDTD method will be unstable due to the perturbation term.