An Efficient Method to Reduce the Numerical Dispersion in the LOD-FDTD Method Based on the (2, 4) Stencil

Abstract

A parameter-optimized (2, 4) stencil based locally-one-dimensional (LOD) finite-difference time-domain (FDTD) is presented with much reduced numerical dispersion errors. The method is first proved to be unconditionally stable. Then by using different optimization schemes, the method is optimized to satisfy different accuracy requirements, such as minimum dispersion errors in the axial directions, in the diagonal direction, and in the specified angles. Performances of the parameter-optimized LOD-FDTD with different time steps and frequencies are also studied. It is found that the parameter optimization can significantly reduce numerical dispersion errors, bringing them down to the level of the conventional FDTD but with the time step exceeding the CFL limit and without much additional computational cost. In addition, the optimized parameters are not sensitive to frequencies; in particular, the optimized parameters obtained at a higher frequency still present low numerical dispersion errors at a lower frequency.