Some computational problems in electromagnetic wave simulations with metamaterials

Metamaterial is an artificially made nano electromagnetic material, whose permittivity and permeability can be both negative for some frequencies. Hence the reflective index of metamaterial is negative. The study of metamaterial started from the beginning of 2000, and has been one of the hottest research topics in the past decade. We focus on introducing those modeling equations appeared in simulating wave propagation in metamaterials and developing effective finite element methods for solving them. This paper is a short survey of the works carried out in the computational mathematics community in the past ten years. In the end, we mention some open problems that worth further study.