Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations

Liping Gao and Shouhui Zhai

Mathematical Problems in Engineering, 2017, vol. 2017, 1-11

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6063176

DOI: 10.1155/2017/6063176

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