Stabilized Mixed Finite-Element Time-Domain Method for Fast Transient Analysis of Multiscale Electromagnetic Problems

This paper describes the mixed E-B finite-element time-domain (FETD) method that is stabilized for an arbitrary time step size. Since the existing mixed FETD (M-FETD) method is based on a fully explicit leapfrog time marching procedure, it has a numerical stability condition: if not satisfied, the instability arises. The condition gives the upper limit of the time step size, and it becomes much strict if there exist small meshes in a computational domain. As a result, the smaller the time step size is, the higher the computational cost becomes. In this paper, we propose the stabilized M-FETD method through developing the stabilization process after specifying the root cause of the instability of the existing method. By virtue of the stabilization process, we can derive the fully explicit updating process which is efficient and numerically stable for the arbitrary time step size without degrading the accuracy. Numerical results of example problems demonstrate that our approach is superior to the existing one, especially in a multiscale electromagnetic problem in two and three dimensions.