A new FDTD formulation with reduced dispersion for the simulation of wave propagation through inhomogeneous media

A discrete vector calculus on a lattice is developed based on primary and dual lattices that support scalar as well as vector fields with collocated components. The resulting discrete vector calculus is applied to electromagnetic theory and is, by construction, consistent with both the integral and differential forms of Maxwell's equations. In its own right, the resulting discrete space-time (DST) method does not hold any particular advantage over the standard Yee algorithm other than improved stability. The the time-domain element (TDE) method is presented, which may be viewed as a reinterpretation and generalization of the Yee algorithm. The formulations of the TDE and DST methods are such that it combination of the two is quite transparent. The combined algorithm has the advantage in that it retains the local nature of each as well as taking advantage of the obvious complementarity of the two. The result is a robust, highly accurate, and efficient algorithm that inherently satisfies boundary conditions on dielectric interfaces.