Modified Splitting FDTD Methods for Two-Dimensional Maxwell's Equations. (22nd February 2017)

• Record Type: Journal Article
• Authors: Gao, Liping; Zhai, Shouhui
• Other Names: Specogna Ruben Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-02-22
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/6063176
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we develop a new method to reduce the error in the splitting finite-difference method of Maxwell's equations. By this method two modified splitting FDTD methods (MS-FDTDI, MS-FDTDII) for the two-dimensional Maxwell equations are proposed. It is shown that the two methods are second-order accurate in time and space and unconditionally stable by Fourier methods. By energy method, it is proved that MS-FDTDI is second-order convergent. By deriving the numerical dispersion (ND) relations, we prove rigorously that MS-FDTDI has less ND errors than the ADI-FDTD method and the ND errors of ADI-FDTD are less than those of MS-FDTDII. Numerical experiments for computing ND errors and simulating a wave guide problem and a scattering problem are carried out and the efficiency of the MS-FDTDI and MS-FDTDII methods is confirmed.