Stable and efficient numerical schemes for two-dimensional Maxwell equations in lossy medium

Highlights: • Two kinds of novel numerical schemes are proposed for 3D Maxwell equations. • The new schemes are more efficient than general finite difference schemes. • The new schemes are energy structure-preserving. • A new skill is used to get the truncation error that is important for convergence. -- Abstract: In this paper, some stable and efficient numerical methods are developed for two-dimensional Maxwell equations. To avoid solving large scale algebraic equations, we use local one-dimensional (LOD) technique and split the original equations into several LOD equations. Then, the resulted LOD equations are discretized by Wendroff scheme which is usually applied to simulate hyperbolic-type equations. The Lie-Trotter composition and Strang composition are employed. To improve the computational efficiency and the convergent accurate, the space direction is approximated by high order compact method. Some benchmark symbols, such as stability, conservation laws of the schemes are analyzed. Some numerical examples confirm the theoretical analysis. Numerical results show that the new schemes can not only accurately simulate the electromagnetic waves, including profiles, amplitude, but also capture the energy structures exactly.