Commun. Comput. Phys., 11 (2012), pp. 1673-1696.


New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D

Liping Gao 1*, Dong Liang 2

1 Department of Computational and Applied Mathematics, School of Sciences, China University of Petroleum, Qingdao, 266555, P.R. China.
2 Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada.

Received 12 November 2010; Accepted (in revised version) 3 June 2011
Available online 12 January 2012
doi:10.4208/cicp.121110.030611a

Abstract

The symmetric energy-conserved splitting FDTD scheme developed in [1] is a very new and efficient scheme for computing the Maxwell's equations. It is based on splitting the whole Maxwell's equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell's equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H^1-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H^1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H^1-norm. Numerical experiments are carried out and confirm our theoretical results.

AMS subject classifications: 65N06, 65N12, 65N15

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Key words: Symmetric EC-S-FDTD, energy-conserved, unconditional stability, super convergence, Maxwell's equations, splitting.

*Corresponding author.
Email: l.gao@upc.edu.cn (L. Gao), dliang@mathstat.yorku.ca (D. Liang)
 

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