Splitting multisymplectic integrators for Maxwell’s equations

✍ Scribed by Linghua Kong; Jialin Hong; Jingjing Zhang

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 848 KB
• Volume: 229
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2010.02.010

✦ Synopsis

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 onedimensional (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.