Modified Splitting FDTD Methods for Two-Dimensional Maxwell’s Equations
Open Access
- 1 January 2017
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2017, 1-11
- https://doi.org/10.1155/2017/6063176
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.Keywords
Funding Information
- Natural Science Foundation of Shandong Province (ZR2014AM029, ZR2013DM015, 16CX02017A)
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