A Hybrid Algorithm Based on FDTD and Spatially filtered FDTD methods for Multiscale Problem

A new hybrid technique based on the traditional finite-difference time-domain (FDTD) algorithm and the spatially filtered FDTD (SF -FDTD) method is developed to analyse 2-D multiscale problem. The FDTD method is used to calculate the electromagnetic fields in coarse grid region, and the SF - FDTD method is utilized in the fine grid region. Due to the controllable stability characteristic of SF -FDTD method, a uniform time step can be chosen to the maximum discrete time step corresponding to the coarse grid in the computation domain. Therefore, the temporal interpolation is no long needed at the boundary of the two grids. In addition, by adjusting the field components distribution in the grid and only filtering electric field components, the effect of the filter operation on the interface between the coarse and fine grids is eliminated, ensuring the precision of the proposed method. The accuracy and efficiency of the proposed method was verified by comparing with the standard FDTD method with the fine grids.