Fast Explicit and Unconditionally Stable FDTD Method for Electromagnetic Analysis

In this paper, a fast explicit and unconditionally stable finite-difference time-domain (FDTD) method is developed, which does not require a partial solution of a global eigenvalue problem. In this method, a patch-based single-grid representation of the FDTD algorithm is developed to facilitate both theoretical analysis and efficient computation. This representation results in a natural decomposition of the curl-curl operator into a series of rank-1 matrices, each of which corresponds to one patch in a single grid. The relationship is then theoretically analyzed between the fine patches and unstable modes, based on which an accurate and fast algorithm is developed to find unstable modes from fine patches with a bounded error. These unstable modes are then upfront eradicated from the numerical system before performing an explicit time marching. The resultant simulation is absolutely stable for the given time step irrespective of how large it is, the accuracy of which is also ensured. In addition, both lossless and general lossy problems are addressed in the proposed method. The advantages of the proposed method are demonstrated over the conventional FDTD and the state-of-the-art explicit and unconditionally stable FDTD methods by numerical experiments.