A Second-Order Symplectic Partitioned Runge-Kutta Scheme for Maxwell's Equations

摘要

In this paper, we construct a new scheme for approximating the solution to infinite dimensional non-separable Hamiltonian systems of Maxwell's equations using the symplectic partitioned Runge-Kutta (PRK) method. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. The scheme preserves the symplectic structure in the time direction and shows substantial benefits in numerical computation for Hamiltonian system, especially in long-term simulations. Also several numerical examples are presented to verify the efficiency of the scheme.