Higher-Order FDTD Methods for Large Problems

Abstract

The Finite-Difference Time-Domain (FDTD) algorithm provides a simple and efficient means of solving Maxwell's equations for a wide variety of problems. In Yee's uniform grid FDTD algorithm the derivatives in Maxwell's curl equations are replaced by central difference approximations. Unfortunately, numerical dispersion and grid anisotropy are inherent to FDTD methods. For large computational domains, e.g., ones that have at least one dimension forty wavelengths or larger, phase errors from dispersion and grid anisotropy in the Yee algorithm (YA) can be significant unless a small spatial discretization is used. For such problems, the amount of data that must be stored and calculated at each iteration can lead to prohibitive memory requirements and high computational cost. To decrease the expense of FDTD simulations for large scattering problems two higher-order methods have been derived and are reported here. One method is second-order in time and fourth-order in space (2-4); the other i..