Unconditionally Stable Leapfrog Adi-FDTD Method for Lossy Media

Abstract

Abstract-This paper presents an unconditionally stable leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method for lossy media. Conductivity terms of lossy media are incorporated into the leapfrog ADI-FDTD method in an analogous manner as the conventional explicit FDTD method since the leapfrog ADI-FDTD method is a perturbation of the conventional explicit FDTD method. Implementation of the leapfrog ADI-FDTD method for lossy media with special consideration for boundary condition is provided. Numerical results and examples are presented to validate the formulation.

Modeling of ultra‐wideband indoor channels with the modified leapfrog ADI‐FDTD method

“…As seen in either (8) or (9), the last term on the right-hand side is mixed-coordinate partial derivatives similar to that shown in [20]; it poses a computational challenge with the Yee grid. Here we show its removal by adding (8) to (9):…”

“…The one-step leapfrog ADI-FDTD method has been shown for its relatively high computational efficiency [15,16]; it has often been applied for lossless media [17][18][19], while in many realistic situations, lossy structures do exist. In [20], a set of equations of the leapfrog ADI-FDTD for treating lossy media has been proposed.…”

“…However, as shown in [20], if a loss (or conductivity) term is directly introduced through the conventional leapfrog ADI derivation, there will be some mixed-coordinate partial derivative terms (e.g., ∂ 2 /∂x∂y), which need to be evaluated numerically; and it poses a computational challenge with the Yee grid. In this paper, we have successfully solved the problem, developed an improved leapfrog ADI-FDTD algorithm, and applied it to model indoor UWB channels with lossy objects.…”

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

“…The leapfrog alternating‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD) method is a recent development of the class of unconditionally stable FDTD methods, which are not restricted by the stability criterion that has limited the capability of the conventional explicit FDTD method for a long time . It is applied to efficiently analyze scattered waves in lossy media as well as wave propagation in electronic bandgap (EBG) structures . These analyses, and many others, usually involve targets and/or materials that allow electromagnetic waves to either penetrate or propagate.…”

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

“…In [11], the leapfrog ADI-FDTD method was also developed for lossy media. But the difference equations are derived by considering the leapfrog ADI-FDTD method as a perturbation of the conventional explicit FDTD method instead of from Maxwell's equations or conventional ADI-FDTD method.…”