Suppression of numerical anisotropy and dispersion with optimized finite-difference time-domain methods

To reduce numerical dispersion in finite-difference time-domain (FDTD) methods, large computational stencils are often used. This paper proposes an optimized two-dimensional method by weighting the (2,4) stencil and the "neighborhood" stencil. After obtaining the amplification factor and the numerical dispersion relation, the optimal value of the weight parameter is obtained to minimize the numerical dispersion at a designated frequency. The anisotropy, dispersion error and the accumulated phase errors are greatly reduced over a broad bandwidth. Both the maximum anisotropy and the maximum dispersion error are 8.9×10^-5, and the accumulated phase error is 0.002367° per cell, respectively, for a broad band of frequencies if optimized at 10 cells per wavelength. Numerical experiments are performed which show very good agreement with theoretical analysis. The time step size bound is the same as for Yee\´s FDTD.