Splitting multisymplectic integrators for Maxwell's equations

  • Authors:

  • Linghua Kong;Jialin Hong;Jingjing Zhang

  • Affiliations:

  • School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, P.O. Box 2719, Beijing 100190, China;State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, P.O. Box 2719, Beijing 100190, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

In the paper, we describe a novel kind of multisymplectic method for three-dimensional (3-D) Maxwell's equations. Splitting the 3-D Maxwell's equations into three local one-dimensional (LOD) equations, then applying a pair of symplectic Runge-Kutta methods to discretize each resulting LOD equation, it leads to splitting multisymplectic integrators. We say this kind of schemes to be LOD multisymplectic scheme (LOD-MS). The discrete conservation laws, convergence, dispersive relation, dissipation and stability are investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, non-dissipative, and of first order accuracy in time and second order accuracy in space. As a reduction, we also consider the application of LOD-MS to 2-D Maxwell's equations. Numerical experiments match the theoretical results well. They illustrate that LOD-MS is not only efficient and simple in coding, but also has almost all the nature of multisymplectic integrators.