Three-Dimensional Unconditionally Stable LOD-FDTD Methods With Low Numerical Dispersion in the Desired Directions

In order to get low numerical dispersion in the desired directions, four-step locally one-dimensional finitedifference time-domain (LOD4-FDTD), five-step LOD-FDTD (LOD5-FDTD), and six-step LOD-FDTD (LOD6-FDTD) methods are developed here. These methods are derived from the threestep LOD-FDTD method, and each of their substeps has variation in either the x-, y-, or z-directions. The LOD4-FDTD, LOD5FDTD, and LOD6-FDTD methods have two substeps in one, two, and three directions, respectively. These methods give low numerical dispersion in the directions in which they have two substeps. In addition, the LOD5-FDTD method gives low anisotropy error (AE) for the directions in which it has two substeps, and the LOD6-FDTD method gives low 3-D AE. Furthermore, to validate the analytical results, the simulation results are given here.