Liping Gao (Coventry. UK)

Analysis of convergence and stability of ADI FDTD algorithm for three-dimensional Maxwell equations

Abstract

In 2000, Zheng, Chen and Zhang proposed an alternating direction implicit finite-difference time-domain (ADI-FDTD) scheme for 3-D Maxwell's equations with lossless materials, which requires only two alternations in soultion marching. In the case of a homogeneous medium, it was proved by Zheng, Chen and Zhang using a Fourier analysis together with the help of significant use of computer-aided algebra that this ADI-FDTD scheme is unconditionally stable. In this paper, this ADI-FDTD scheme is extended to the case of a lossy medium. The unconditional stability and first order convergence of our scheme are proved using the energy method together with the spliting of the Maxwell's equations. In the special case of lossless medium, our results show that the ADI-FDTD scheme of Zheng-Chen-Zhang is unconditionally stable and second-order convergent.