A new FDTD stencil for reduced numerical anisotropy in the computer modeling of wave phenomena

Abstract

An isotropic finite difference scheme is utilized for the development of a new stencil for the finite-difference time-domain (FDTD) modeling of electromagnetic wave propagation. The key attribute of the new stencil is the improved isotropy of the numerical phase velocity at fairly moderate spatial sampling of the fields. More specifically, for a given phase velocity anisotropy error, the new stencil requires a much coarser grid than the one required by the standard, second-order accurate FDTD stencil. This, in turn, amounts to gains in computational resources when transient electromagnetic interactions in electrically-large domains are being modeled. The numerical attributes of the proposed stencil, namely, its dispersion, anisotropy and stability, are presented in the context of its application to the numerical simulation of two-dimensional transient electromagnetic wave propagation. Through a series of numerical studies, the enhanced isotropy provided by the proposed scheme is demonstrated and contrasted in a quantitative manner to that of the standard FDTD stencil. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.