A Conformal Energy-Conserved Method for Maxwell's Equations with Perfectly Matched Layers (Communications in Computational Physics, 2018)
In this paper, a conformal energy-conserved scheme is proposed for solvingthe Maxwell's equations with the perfectly matched layer. The equations are split as aHamiltonian system and a dissipative system, respectively. The Hamiltonian systemis solved by an energy-conserved method and the dissipative system is integrated exactly.With the aid of the Strang splitting, a fully-discretized scheme is obtained. Theresulting scheme can preserve the five discrete conformal energy conservation lawsand the discrete conformal symplectic conservation law. Based on the energy method,an optimal error estimate of the scheme is established in discrete L2-norm. Some numericalexperiments are addressed to verify our theoretical analysis.