超材料电磁波有限元模拟中的相关问题 献给林群教授80华诞

Some computational problems in electromagnetic wave simulations with metamaterials

超材料是指一种人工合成的纳米电磁材料,它的介电常数和磁导率对某些波频段会同时为负,从而导致其折射率为负.超材料硏究的兴起始于2000年,在过去的十多年一直是多个学科的研究热点.本文侧重介绍电磁波在超材料中传播所涉及的模型方程以及如何用有限元方法求解.本文是对过去十年来计算数学在此领域工作的一个总结.最后提出一些值得继续探讨的问题.

Metamaterial is an artificially made nano electromagnetic material, whose permittivity and perme- ability 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.