Energy Stable Splitting Schemes for Maxwell’s Equations in Lorentz Media

Abstract

In this paper, we introduce energy-stable schemes based on operator splitting methods for Maxwell’s equations in two-dimensional Lorentz dispersive media with transverse electric polarization, namely the sequential splitting scheme (SS-ML) and the Strang-Marchuk splitting scheme (SM-ML). Each splitting scheme involves two substages per time step, where 1D discrete sub-problems are solved using the Crank-Nicolson method for time discretization. Both schemes ensure energy decay and unconditional stability. The convergence analysis reveals that the SS-ML scheme exhibits first-order accuracy in time and second-order accuracy in space based on the energy technique, while the SM-ML scheme achieves second-order accuracy in both time and space. Additionally, numerical dispersion analysis yields two discrete numerical dispersion relation identities for each scheme. Theoretical results are supported by examples and numerical experiments.