Optimized finite-difference time-domain methods based on the (2,4) stencil

Abstract

The higher order (2,4) scheme optimized in terms of Taylor series in the finite-difference time-domain method is often used to reduce numerical dispersion and anisotropy. This paper investigates optimization of the numerical dispersion behavior for a square Yee mesh based on the (2,4) computational stencil. It is shown that, for one designated frequency, numerical dispersion can be eliminated for some directions of travel, such as the coordinate axes or the diagonals, or numerical anisotropy can be eliminated entirely, resulting in a constant "residual" numerical dispersion. Using a coefficient-modification technique, the residual numerical dispersion can then be completely eliminated at that frequency, or for a wide-band signal, the numerical dispersion error and the averaged-accumulated phase error can be minimized. The stability of the method is analyzed, the numerical dispersion relation is given and validated using numerical experiments, and the relative rms errors are compared to the standard (2,4) scheme for the proposed methods. The optimized methods are second-order accurate in space and have higher accuracy than the standard (2,4) scheme. It has been found that the dispersion error of the (2,4) scheme is like that of a second-order accurate method, though it behaves like a fourth-order accurate method in terms of anisotropy.