Stability of FDTD on nonuniform grids for Maxwell’s equations in lossless media

In this paper we present practical stability conditions for the finite-difference time-domain method on nonuniform tensor product grids (Yee grids). These stability conditions apply to Maxwell’s equations for inhomogeneous and lossless media. Rectangular domains are considered and the conditions are expressed in terms of the minimum spatial stepsizes of the grid and the maximum electromagnetic wave speed in the configuration. The maximum wave speed is known as soon as the media are specified, while the minimum spatial stepsizes are known after the configuration has been discretized. For two-dimensional configurations we present a number of numerical examples which illustrate the effectiveness of the proposed stability conditions.