A Conformal Energy-Conserved Method for Maxwell’s Equations with Perfectly Matched Layers

Abstract

In this paper, a conformal energy-conserved scheme is proposed for solving the Maxwell's equations with the perfectly matched layer. The equations are split as a Hamiltonian system and a dissipative system, respectively. The Hamiltonian system is 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. The resulting scheme can preserve the five discrete conformal energy conservation laws and the discrete conformal symplectic conservation law. Based on the energy method, an optimal error estimate of the scheme is established in discrete L 2-norm. Some numerical experiments are addressed to verify our theoretical analysis.

Ergodic numerical approximations for stochastic Maxwell equations

“…The damping terms σE and σH may be induced by conductivity of the medium or by the perfectly matched layer technique (see e.g. [15,19]). It is assumed that σ ∈ W 1,∞ (D) and σ ≥ σ 0 > 0 for a constant σ 0 .…”