Commun. Comput. Phys., 6 (2009), pp. 804-825.


Symmetric Energy-Conserved Splitting FDTD Scheme for the Maxwell's Equations

Wenbin Chen 1*, Xingjie Li 2, Dong Liang 3

1 School of Mathematical Sciences, Fudan University, Shanghai, 200433, China.
2 School of Mathematical Sciences, Fudan University, Shanghai, 200433, China; School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
3 Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada.

Received 22 June 2008; Accepted (in revised version) 19 January 2009
Available online 5 March 2009

Abstract

In this paper, a new symmetric energy-conserved splitting FDTD scheme (symmetric EC-S-FDTD) for Maxwell's equations is proposed. The new algorithm inherits the same properties of our previous EC-S-FDTDI and EC-S-FDTDII algorithms: energy-conservation, unconditional stability and computational efficiency. It keeps the same computational complexity as the EC-S-FDTDI scheme and is of second-order accuracy in both time and space as the EC-S-FDTDII scheme. The convergence and error estimate of the symmetric EC-S-FDTD scheme are proved rigorously by the energy method and are confirmed by numerical experiments.

AMS subject classifications: 65N10, 65N15, 78M20

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Key words: Maxwell's equation, ADI method, FDTD, energy-conserved, second-order accuracy, symmetric scheme.

*Corresponding author.
Email: wbchen@fudan.edu.cn (W. Chen), xingjieli@fudan.edu.cn (X. Li), dliang@mathstat.yorku.ca (D. Liang)
 

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