Unconditionally stable implicit finite-difference time-domain method

An implicit finite-difference time-domain method (FDTD) using the principle of the alternating direction implicit (ADI) technique is introduced. The method is unconditionally stable, and the maximum time-step size is not limited by the Courant-Friedrich-Levy (CFL) condition, but rather by numerical errors. Compared with the conventional FDTD method, the time-step size of ADI-FDTD can be much larger, so the simulation time is shortened, especially when the grid size is much smaller than wavelength. The perfect matched layer (PML) technique is used in ADI-FDTD calculation for the first time. The expressions for the exponential time-stepping algorithm in PML are derived. The ADI-FDTD method is validated by an example.