Explicit and Unconditionally Stable FDTD Method Without Eigenvalue Solutions

Existing explicit and unconditionally stable FDTD methods rely on a partial eigenvalue solution of a global system matrix to find the unstable modes that cannot be stably simulated by the given time step. In this paper, we develop a fast explicit and unconditionally stable FDTD method requiring no global eigenvalue solutions. In this method, we find the relationship between the unstable modes and the fine meshes, and use this relationship to directly identify the source of instability. We then upfront eradicate the source of instability 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. If the time step is chosen based on accuracy, the accuracy of the proposed method is also guaranteed. Numerical experiments have demonstrated a significant speedup of the proposed method over the conventional FDTD as well as state-of-the-art explicit and unconditionally stable methods.