Applications of Nonstandard Finite Difference Models to Computational Electromagnetics

Abstract

We introduce an exact nonstandard finite-difference model of the one-dimensional absorbing wave equation, and use it to develop a high accuracy version of the finite-difference time-domain (FDTD) algorithm to solve the absorbing wave equation and the conducting Maxwell's equations in two and three dimensions. For grid spacing h, and wavelength λ, the solution error of the ordinary FDTD algorithm is because it uses second-order central finite difference approximations. By exploiting the analytical properties of decaying-harmonic solution basis functions in a nonstandard finite difference model we reduce the error to without using higher order finite differences. We have verified the accuracy of the algorithms by comparing with analytic solutions of near-field Mie scattering, and have used them to investigate the optical properties of subwavelength conductive diffraction gratings.