UNIFIED EFFICIENT FUNDAMENTAL ADI-FDTD SCHEMES FOR LOSSY MEDIA

This paper presents the unifled e-cient fundamen- tal alternating-direction-implicit flnite-difierence time-domain (ADI- FDTD) schemes for lossy media. The schemes presented include aver- aging, forward-forward, forward-backward and novel exponential time difierencing schemes. Uniflcations of these schemes in both conven- tional and e-cient fundamental forms of source-incorporated ADI- FDTD are provided. In the latter, they are formulated in the sim- plest, most concise, most e-cient, and most fundamental form of ADI-FDTD. The unifled update equations and implementation of the e-cient fundamental ADI-FDTD schemes are provided. Such e-cient fundamental schemes have substantially less right-hand-side update co- e-cients and fleld variables compared to the conventional ADI-FDTD schemes. Thus, they feature higher e-ciency with reduced memory indexing and arithmetic operations. Other aspects such as fleld and parameter memory arrays, perfect electric conductor and perfect mag- netic conductor implementations are also discussed. Numerical results in the realm of CPU time saving, asymmetry and numerical errors as well as speciflc absorption rate (SAR) of human skin are presented.