Stability analyses of non-uniform time-step schemes for ADI- and LOD-FDTD methods

This paper presents the stability analyses of the non-uniform time-step (NUTS) schemes for alternating direction implicit-(ADI-) and locally one-dimensional finite-difference time-domain (LOD-FDTD) methods. Unlike the previous unconditionally stable FDTD methods, different (non-uniform) time steps may be used for different periods during simulation. The stability based on Fourier amplification matrices for both NUTS ADI- and LOD-FDTD methods is investigated. The numerical stability analyses show that the NUTS scheme for ADI-FDTD method may yield unstable results, while the NUTS scheme for LOD-FDTD method is stable. This is an advantage of LOD-FDTD method over ADI-FDTD method in addition to its higher computational efficiency.