Simulation of eletromagnetic wave propagation in three-dimensional media by an FDTD method

We have developed a finite-difference time-domain solution to Maxwell's equations for simulating electromagnetic wave propagation in three-dimensional media. The algorithm allows arbitrary variations of electrical conductivity and permittivity within a model. We use the Vee's staggered grid technique to sample the fields and approximate the spatial derivatives with optimized second-order finite differences everywhere except close to the computational domain boundary where we use conventional central differences instead. The pointwise computational time of the optimized second-order difference scheme is the same as that of the conventional fourth-order difference scheme, but the former has better dispersion characteristics. Although the optimized difference scheme imposes stricter limitations on the size of time steps allowed for an explicit time-marching scheme, a simple calculation shows that this scheme is more cost-effective, due to its lower required spatial sampling rate, than the conventional second- or fourth-order difference scheme. The temporal derivatives are approximated by second-order central differences throughout.