Year: 2011
Author: Huajun Zhu, Songhe Song, Yaming Chen
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 6 : pp. 663–688
Abstract
In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell's equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.11-m1183
Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 6 : pp. 663–688
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Multi-symplectic wavelet collocation method Maxwell's equations symplectic conservation laws.
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