One-Step Absolutely Stable FDTD Methods for Electromagnetic Simulation

Abstract

As the explicit finite-difference time-domain (FDTD) method is restricted by the wellknown Courant-Friedruchs-Lewy (CFL) stability condition and is inefficient for solving numerical tasks with fine structures, various implicit methods have been proposed to tackle the problem, while many of them adopt time-splitting schemes that generally need at least two sub-steps to finish update at a full time step, and the strategies used seem to be an unnatural habit of computation compared with the most widely-used one-step methods. The procedure of splitting time step also reduces computational efficiency and makes implementation of these algorithms complex. In the present paper, two novel one-step absolutely stable FDTD methods including one-step alternating-direction-implicit (ADI) and one-step locally-one-dimensional (LOD) methods are proposed. The two proposed methods are derived from the original ADI-FDTD method and LOD-FDTD method through some linear operations applied to the original methods and are algebraically equivalent to the original methods respectively, but they both avoid the appearance of intermediate fields and are one-step method just like the conventional FDTD method. Numerical experiments are carried out for validation of the two proposed methods, and from the numerical results it can be concluded that the proposed methods can solve equation correctly and are simpler than the original methods, and their computation efficiency is close to that of the existing one-step leapfrog ADI-FDTD method.