Multisymplectic Preissman scheme for the time-domain Maxwell's equations

From the Bridges' multisymplectic form of Maxwell's equations, we derive a multisymplectic Preissman scheme which couples two time levels for 2+1 dimensional Maxwell's equations. The scheme is proven to preserve the discrete local energy exactly. Numerical results are reported to illustrate that the scheme is effective and it can get more precise numerical solutions than Yee's scheme. Our numerical results can also indicate that the scheme keeps the discrete local energy and the global energy very well.