Generation of 2-D FDTD schemes in the spectral domain

Traditionally, FDTD schemes are generated in the spatial/temporal domains. This paper presents a new methodology in which existing and new FDTD schemes are generated in the spectral domain. The principles of the new methodology are introduced. The new methodology merits are demonstrated through its application to the 2-D standard Yee algorithm, the nine point stencil nonstandard FDTD (NSFDTD) and the hexagonal mesh based FDTD (HFDTD). It is shown that the concept of spectral order of accuracy (SOoA), defined within the new methodology, enables the concise treatment and control of order of accuracy (OoA), numerical dispersion and numerical anisotropy of FDTD schemes.