Global energy-preserving local mesh-refined S-FDTD schemes for two dimensional Maxwell's equations in Drude metamaterials

Abstract

Modeling electromagnetic propagation in metamaterials is of importance in many applications. Designing efficient local mesh refinements is crucial to improve the resolution capacity of solution for solving Maxwell's equations within metamaterials and it is a difficult task to develop local mesh-refined schemes for preserving global energy across the interfaces between coarse and fine meshes. In this paper, we develop two global energy-preserving local mesh-refined splitting FDTD schemes for Maxwell's equations with Drude model. By combining with the energy-conserved splitting FDTD methods, the local mesh-refined interface schemes are established on the interfaces of coarse and fine meshes, which ensure global energy preserving. We prove that the developed GEP-LMR-S-FDTD schemes satisfy global energy conservation and are unconditionally stable. Meanwhile, fast implementation of the GEP-LMR-S-FDTD schemes is investigated to compute the metamaterial electromagnetic problems. Numerical experiments show the excellent performance of the schemes.