A review of weakly conditional stable finite‐difference time‐domain method for modeling electromagnetic problems with fine structures

Abstract

The finite‐difference time‐domain (FDTD) method has been proven to be an effective tool for simulating varieties of electromagnetic interaction problems. However, because the Courant‐Friedrich‐Levy condition must be satisfied in this method, its maximum time step size is limited by the minimum size of cell used in the computational domain. So, the FDTD method is inefficient to analyze the electromagnetic problem, which has very fine structures. To deal with this problem, the weakly conditional stable (WCS)‐FDTD method is developed. In the WCS‐FDTD method, the confinement of the fine spatial meshes on the time step size is removed by using the hybrid implicit explicit difference in the directions with fine structures. So, this method has much higher computational efficiency than the FDTD method and is extremely useful for the problems that have fine structures in 2 directions. In this paper, the fundamental theory, including the basic formulations, time stability condition, dispersion error, and absorbing boundary condition of the WCS‐FDTD method are presented. Some applications and important developments of this method are provided, and future possibilities of this method are discussed.