Recent progress on mathematical analysis and numerical simulations for Maxwell's equations in perfectly matched layers and complex media: a review

Abstract

In this paper, we presented a review on some recent progress achieved for simulating Maxwell's equations in perfectly matched layers and complex media such as metamaterials and graphene. We mainly focused on the stability analysis of the modeling equations and development and analysis of the numerical schemes. Some open issues were pointed out, too.

Keywords

• maxwell's equations
• finite element method
• fdtd method
• invisibility cloak
• metamaterials
• perfectly matched layer
• graphene