Unified efficient fundamental ADI-FDTD schemes for lossy media

Abstract

This paper presents the unified efficient fundamental alternating-direction-implicit finite-difference time-domain (ADIFDTD) schemes for lossy media. The schemes presented include averaging, forward-forward, forward-backward and novel exponential time differencing schemes. Unifications of these schemes in both conventional and efficient fundamental forms of source-incorporated ADIFDTD are provided. In the latter, they are formulated in the simplest, most concise, most efficient, and most fundamental form of ADI-FDTD. The unified update equations and implementation of the efficient fundamental ADI-FDTD schemes are provided. Such efficient fundamental schemes have substantially less right-hand-side update coefficients and field variables compared to the conventional ADI-FDTD schemes. Thus, they feature higher efficiency with reduced memory indexing and arithmetic operations. Other aspects such as field and parameter memory arrays, perfect electric conductor and perfect magnetic conductor implementations are also discussed. Numerical results in the realm of CPU time saving, asymmetry and numerical errors as well as specific absorption rate (SAR) of human skin are presented.