Relative accuracy of several finite-difference time-domain methods in two and three dimensions

A comparison of the accuracy of several orthogonal-grid finite-difference-time-domain (FDTD) schemes is made in both two and three-dimensions. The relative accuracy is determined from the dispersion error associated with each algorithm and the number of floating-point operations required to obtain a desired accuracy level. In general, in both 2-D and 3-D, fourth-order algorithms are more efficient than second-order schemes in terms of minimizing the number of computations for a given accuracy level. In 2-D, a second-order approach proposed by Z. Chen et al. (1991) is much more accurate than the scheme of K.S. Yee (1966) for a given amount of computation, and can be as efficient as fourth-order algorithms. In 3-D, Yee's algorithm is slightly more efficient than the approach of Chen et al. in terms of operations, but much more efficient in terms of memory requirements.<>