On the design of leapfrog integrators for optimized implementations of 3D FDTD models

In this paper the formulation of modified leapfrog integrators for three-dimensional (3D) finite-difference time-domain (FDTD) simulations is discussed. We propose an approach that introduces a parametric variant of the fourth-order approach, and aims at preserving the exact dispersion characteristics at the discrete level, via proper manipulation of its spatial part. The entailed computational cost is not altered, and wave propagation is reproduced more accurately via the new version of the integrator, especially when the latter is combined with spatial operators of similar calibre.