Implicit Finite Difference Time Domain Methods

The efficiency of the conventional, explicit finite difference time domain (FDTD) method is constrained by the upper limit on the temporal discretization imposed by the Courant-Friedrich-Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing implicit, unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. This work presents a novel three-dimensional frequency dependent fully implicit Crank Nicolson FDTD method. A modified frequency dependent alternating direction implicit FDTD (FD-ADI-FDTD) method, having better accuracy than the normal FD-ADI-FDTD method, is also presented.