Numerical dispersion analysis of a multi-symplectic scheme for the three dimensional Maxwell's equations

Authors:
Wenjun Cai;Yushun Wang;Yongzhong Song
Affiliations:
Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics and Sciences, Nanjing Normal University, Nanjing 210046, China;Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics and Sciences, Nanjing Normal University, Nanjing 210046, China;Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematics and Sciences, Nanjing Normal University, Nanjing 210046, China
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

In this paper, we study a multi-symplectic scheme for three dimensional Maxwell's equations in a simple medium. This is a system of PDEs with multi-symplectic structures. We prove that this multi-symplectic scheme preserves the discrete version of local and global energy conservation law and the discrete divergence. Furthermore, we extend the discussion to several dispersion properties of the multi-symplectic scheme including the numerical dispersion relation, the numerical group velocity, the effect of large time steps and the CFL condition.