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Multi-Symplectic Wavelet Collocation Method for Maxwell’s Equations

Published online by Cambridge University Press:  03 June 2015

Huajun Zhu ,
Songhe Song  and
Yaming Chen
Huajun Zhu*
Affiliation:
Department of Mathematics and System Science, School of Science, National University of Defense Technology, Changsha 410073, China
Songhe Song*
Affiliation:
Department of Mathematics and System Science, School of Science, National University of Defense Technology, Changsha 410073, China
Yaming Chen*
Affiliation:
Department of Mathematics and System Science, School of Science, National University of Defense Technology, Changsha 410073, China
*
Corresponding author. Email: girl-zhu@163.com
Email: shsong@nudt.edu.cn
Email: chenym-08@163.com
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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.

Keywords

37M1565P1065M7065T60Multi-symplecticwavelet collocation methodMaxwell’s equationssymplecticconservation laws
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 6 , December 2011 , pp. 663 - 688
Copyright
Copyright © Global-Science Press 2011

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