Splitting of Material Cells and Averaging Properties to Improve Accuracy of the FDTD Method at Interfaces

Abstract

In this paper we present a simple modification to the traditional Finite Difference Time Domain (FDTD) method for treating material cells. The Yee cell is split into 8 smaller material subcells so that each E and H field point is considered to be located at the crosspoint of 8 cells with differing material properties. Thus there is no longer an overlap of the material cells associated with the components of the E and H fields. The 8 material properties are averaged at each crosspoint. Since the averaging is done outside the time marching loop there is little increase in the total computational time. Numerical results are shown for a sinusoidal plane wave scattering from a dielectric sphere. These results are compared with the exact Mie solution and the traditional material cell method along different cuts through the sphere. The splitting and averaging is shown to give improved amplitude accuracy in the vicinity of the sphere. Improvement is also observed at planar interfaces angled with respect to the grid. An additional benefit of this subcell formulation is that objects may be modeled with twice the geometrical resolution without increasing the size of the staggered grid.