Energy evolution of multi-symplectic methods for Maxwell equations with   perfectly matched layer boundary
  In this paper, we consider the energy evolution of multi-symplectic methods for three-dimensional (3D) Maxwell equations with perfectly matched layer boundary, and present the energy evolution laws of Maxwell equations under the discretization of multi-symplectic Yee method and general multi-symplectic Runge-Kutta methods. 
Jialin Hong and Lihai Ji
math.NA