A novel subgridding technique for unconditionally stable time domain method

For inhomogeneous electromagnetic (EM) problems, subgridding techniques have been introduced [1, 2], in which coarse grid is used for homogeneous background, while fine grid is employed in the denser area. In the traditional approach, the interface between the two areas is considered as the boundary condition by each other. Recently, a new subgridding technique called HSG (Huygens sub-griding) method is proposed by Berenger [3], in which the physical connection between two areas is realized by means of Huygens surfaces. Instead of EM components, equivalent currents on the Huygens surface become the commuter between the coarse and fine grid regions. In a macroscopic view, EM fields are teleported from the coarse grid region (source domain) to the fine grid one (problem domain) via equivalent currents. The two major features HSG achieved are arbitrarily large spatial ratio and insignificant spurious reflection from the interface. However the drawback of the late time instability restricts its applicability. The oscillation period associated with this phenomenon depends on the spatial size of the source domain and the ratio between time step and the Courant limit.