Development of optimized operators based on spherical-harmonic expansions for 3D FDTD schemes

Abstract

The subject of this paper pertains to the construction of finite-difference expressions with minimized, as well as controllable discretization errors, suitable for 3D FDTD simulations in large-scale setups. The proposed spatial approximations are designed to mimic the behavior of the exact operators, when applied to plane-wave trial functions. To eliminate undesirable directional dependencies, the expansion of proper error formulae in terms of spherical harmonic functions is performed, which facilitates accuracy improvement and produces optimized operator coefficients in closed-form expressions. The combination of the new operators with low- as well as high-order time integrators yields efficient space-time discrete models, whose reliability renders them desirable substitutes for other traditional solutions.