Commun. Comput. Phys.,
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Volume 4.


Splitting Finite Difference Methods on Staggered Grids for the Three-Dimensional Time-Dependent Maxwell Equations

Liping Gao 1, Bo Zhang 2*, Dong Liang 3

1 School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China.
2 Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China.
3 Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada.

Received 22 July 2007; Accepted (in revised version) 5 January 2008
Available online 27 March 2008

Abstract

In this paper, we study splitting numerical methods for the three-dimensional Maxwell equations in the time domain. We propose a new kind of splitting finite-difference time-domain schemes on a staggered grid, which consists of only two stages for each time step. It is proved by the energy method that the splitting scheme is unconditionally stable and convergent for problems with perfectly conducting boundary conditions. Both numerical dispersion analysis and numerical experiments are also presented to illustrate the efficiency of the proposed schemes.

AMS subject classifications: 65N10, 65N15

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Key words: Splitting scheme, alternating direction implicit method, finite-difference time-domain method, stability, convergence, Maxwell's equations, perfectly conducting boundary.

*Corresponding author.
Email: lipinggao68@gmail.com (L. Gao), b.zhang@amt.ac.cn (B. Zhang), dliang@mathstat.yorku.ca (D. Liang)
 

The Global Science Journal