超材料数值模拟及应用

项目名称： 超材料数值模拟及应用

项目编号： No.11271310

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李继春

作者单位： 湘潭大学

项目金额： 60万元

中文摘要： 在2000年,美国UC-San Diego大学的物理学家功地构造了一种人工纳米材料，其介电常数及磁导率可同时为负，从而得到所谓的负折射率超材料。从2000年后因其独特的特性，超材料的研究引起了各行业科学家与工程师的关注。这里，我们计划通过数值模拟来研究电磁波在超材料中的传播及其应用。数值模拟在超材料的设计及应用中起着非常重要的作用。例如，在2006年10月，美国Duke大学的研究者通过数值模拟成功地设计出一个二维的隐身装置。然而，工程师们提出的超材料模型从未被数学家严格证明其正确性。由于其耗散性及弥散性，超材料的控制方程比传统的空气介质中的Maxwell方程要复杂得多。考虑到所有未知量都是三维并且随时间变化，精确而有效地求解超材料方程是十分困难的，亟需数学家的参与。我们的目标是发展一系列数学上正确，并且高效而精确的时域有限元算法，用来模拟波在超材料中的传播及应用。

中文关键词： 超材料；时域有限元；电磁波隐身；Maxwell 方程；

英文摘要： In 2000, a group of physists at UC-San Diego successfully constructed an artificial nano-material, which has both negative permittivity and permeability, thus obtained the so-called negative refraction index metamaterial for the first time. Due to some exotic properties of metamaterials,the study of metamaterials have attracted scientists and engineers from various areas since 2000.In this project,we plan to investigate how the eletromagnetic wave propagates in metamaterials and some applications of metamaterials.It is known that computer simulation of metamaterials plays a very important role in the construction and application of metamaterials.For example, in October 2006, researchers from Duke University of USA successfully designed a 2D cloaking device through the numerical simulation.However, the well-posedness of those metamaterial models proposed by engineers have never studied by mathematicians yet. Because of dispersivity,the governing equations of metamaterials become much more complicated than the standard Maxwell's equations in free space. Furthermore, since all unknowns are in three-dimensional space and time-dependent, solving the metamaterial Maxwell's equations accuratly and efficiently is very challenging. Our goal of this project is to develop a series of mathematically robust,efficient and acc

英文关键词： Metamaterials；time-domain finite element methods；invisibility cloak；Maxwell's equations；