An Explicit and Unconditionally Stable FDTD Method for Electromagnetic Analysis

Abstract

In this paper, an explicit and unconditionally stable finite-difference time-domain (FDTD) method is developed for electromagnetic analysis. Its time step is not restricted by the space step, and its accuracy is ensured for the time step chosen based on accuracy. The strength of the conventional explicit FDTD is thus preserved in avoiding a system matrix solution, while the shortcoming of the conventional FDTD is eliminated in the time step's dependence on space step. Numerical experiments in both 2-D and 3-D simulations have demonstrated the performance of the proposed method in stability and efficiency without sacrificing accuracy. Index Terms-Explicit methods, finite-difference time-domain (FDTD) method, unconditionally stable methods.

An alternative method for making an explicit FDTD unconditionally stable

“…It is found in [5] that the root caus e of the instability of (1) and (2) is the eigenrnodes of M that have the following eigenvalues :…”

“…Once the uns table eigenrnodes are removed, the FDTD simulation becomes stable. The removal of the uns table eigenrnodes in [5] is achieved by expanding the field solution in the space of stable eigenrnodes and projecting the numerical sys tem onto the same space. In this work, we propos e to directly adapt the numerical sys tem to eradicate the root caus e of the ins tability.…”

“…Compared to [5] in which the stable modes are found to make an explicit FDTD simulation stable, in this work, we find the unstable modes for the given time step and us e them to directly update the FDTD numerical sys tem to be free of the source of ins tability. In many problems where FDTD suffers from the small time step is s ue, the fine features relative to working wavelengths only occupy a small portion of the entire dis cretization, and hence the propos ed new method is particularly efficient since the number of uns table modes is much smaller than the number of stable modes .…”

“…However, they require a matrix solution, the efficiency of which is not desired when a large problem size is encountered. Recently, advanced research has been pursued to addres s the time step problem in the framework of the original explicit time-domain method [2][3][4][5]. In [5], the root caus e of ins tability of an explicit FDTD is identified, bas ed on which an explicit and unconditionally stable FDTD method is developed.…”

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

“…Yet an alternative approach to tackle the multiscale problem has recently been proposed in [8]. This method does not modify the field solutions, but searches the space of stable eigenmodes of the discrete curl-curl operator.…”