Unified Efficient Fundamental Adi-FDTD Schemes for Lossy Media

Abstract

Abstract-This paper presents the unified efficient fundamental alternating-direction-implicit finite-difference time-domain (ADI-FDTD) 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 ADI-FDTD 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.

On the field leakage of the leapfrog ADI‐FDTD method for nonpenetrable targets

“…The leapfrog ADI‐FDTD method for lossy media can be derived from the conventional forward–backward ADI‐FDTD method for lossy media. Unfortunately, previous studies on the forward–backward ADI‐FDTD method reveal that it has nonphysical field leakage when modeling nonpenetrable targets, that is, perfect electric conductor or perfect magnetic conductor . Consequently, the accuracy of electromagnetic waves within such nonpenetrable targets may be compromised as the waves leak into the target in a nonphysical manner.…”

“…However, analyses of the leapfrog ADI‐FDTD method on nonpenetrable targets, which are often of interest for electromagnetic compatibility problems, have not been performed. Such analysis is necessary and important as it has been previously determined that nonphysical field leakage may occur for nonpenetrable targets .…”

Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media

“…Several schemes for the formulation of lossy media have been recently unified for the fundamental ADI-FDTD method [9]. The fundamental ADI-FDTD method has right-hand-side free of matrix operator, and thus it is simpler and more efficient than the conventional ADI-FDTD method.…”

One-Step Leapfrog Adi-FDTD Method for Lossy Media and Its Stability Analysis

“…On the other hand, both the FDTD and ADI-FDTD methods are widely studied for lossy media [7][8][9][10]. In [11], the leapfrog ADI-FDTD method was also developed for lossy media.…”