A Three-Dimensional Unconditionally Stable Five-Step LOD-FDTD Method

A three-dimensional unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD-FDTD) method is presented. Unlike the two-step LOD-FDTD and three-step LOD-FDTD methods, the proposed method has second order temporal accuracy. Hence, it gives less numerical dispersion than the two-step LOD-FDTD and three-step LOD-FDTD methods. It also gives less numerical dispersion than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method. Moreover, for every propagation angle, it provides very small anisotropy error than the above-mentioned FDTD methods. Effects of the time step and the mesh size on the performance of the proposed method are discussed in detail. In this paper, validation of the stability and the accuracy of the proposed method is done with the help of simulation results. To further show the advantage of the proposed method, performance of the proposed method with artificial coefficients (control parameters) is also discussed in this paper.