Development and Investigation of Finite Difference Time Domain Methods on Grids Other than Simple Cubic

Abstract

Simulations are an important part of all areas of engineering, and electromagnetics is no exception. Finite-difference time-domain (FDTD) method has proven to be an attractive numerical method for simulating electromagnetic problems over the past few decades. There are certain drawbacks to the standard FDTD, namely: numerical dispersion and poor handling of anisotropic materials. To alleviate the numerical dispersion problem, the finite-difference time-domain method is derived on face-centered cubic (FCC) lattice as opposed to the standard cubic lattice. Several examples are presented to demonstrate the stability and accuracy of the proposed method. To address the other issue, handling anisotropic materials, an alternative grid known as Lebedev has previously been proposed. In this work, accurate implementation of perfect electric conducting boundary conditions on this grid, and two different techniques to couple Lebedev to the standard method for savings in memory will be presented, and supported by examples.