Explicit Stability Conditions for FDTD on Nonuniform Tensor-Product Grids

In this paper we present sufficient conditions for stability of the finite-difference time-domain method on nonuniform tensor-product grids. The general Courant-Friedrichs-Lewy stability condition can be written in terms of the spectral radius of the first-order Maxwell system matrix. In this paper we present upper bounds for this spectral radius and we use these bounds to obtain sufficient conditions for stability of FDTD in one, two, and three dimensions. The stability conditions are all presented in terms of the maximum electromagnetic wave speed present in the configuration and the minimum step sizes of the grid. Moreover, our conditions reduce to the well-known stability conditions for FDTD if the grid is uniform.