电磁散射中的反问题与隐形涂层的研究

The project aims to study analytically and numerically some key issues of inverse problems and invisibility cloaking for the electromagnetic (EM) scattering. Research on inverse electromagnetic scattering and invisibility cloaking is central to many areas of science and technology, such as radar and sonar, geophysical exploration, medical surgery, non-destructive testing and wireless communication etc. There have been extensive and intensive studies in the literature. However, there are lots of theoretical and computational challenges due to the peculiar structures possessed by those problems. The central goal of this project is to establish the unique determination results in various circumstances, to develop practical reconstruction schemes, and to develop and analyze practical cloaking schemes. The main tools used are analysis and computation. Specifically, the proposed research shall be devoted to the following problems. 1)We will establish the unique determination of permittivity, permeability and conductivity tensors in the real analytic class up to a gauge transformation. 2)We will establish the qualitative unique determination of EM inclusions by scattering measurements. 3)We will develop practical numerical reconstruction schemes by optimal measurement data with very little a priori knowledge of the target scatterer. 4)We will design and analyze regularized approximate invisibility cloaks by nonsingular EM mediums. 5)We will derive the borderline of visibility and invisibility and answer the fundamental question whether or not invisibility will develop singularities of EM parameter tensors. 6)We will develop e_ective and e_cient numerical methods to numerically study the cloaking problems. These problems present interesting challenges from both analytical and computational points of view. The results obtained in this project could find important applications in many real-world fields, and the mathematical and computational techniques developed are widely applicable to other study of electromagnetism.

本项目的主旨是从数学理论和科学计算的角度研究电磁反散射和电磁隐形中的几个关键问题.逆电磁散射和隐形涂层的研究是很多科技领域的核心,如:雷达、声纳、地理勘探、医疗成像、无线通讯等.由于这些问题具有的特殊结构,严重制约了相关研究的进展.本项目将致力于以下几个问题的研究:1)在规范变化的意义下研究确定实解析类中介电常数、磁导率和电导率三类张量的唯一性;2)建立关于一般电磁散射体定性的唯一性结论;3)在已知目标散射体极少信息的条件下,通过优化测量数据建立一类快速稳定数值重构算法;4)通过正则化思想,利用非奇异的电磁介质设计能达到近似隐形效果的隐形涂层;5)严格地推导隐形实现中可见和不可见的界限,并回答完美隐形是否一定要用奇异材料的问题;6)开发一类有效的数值算法与程序包来研究隐形问题.上述问题在许多领域都能找到重要的应用,本项目的理论和数值方法也可以扩展到电磁学的其它领域中.

本项目的主旨是从数学理论和科学计算的角度研究电磁反散射和电磁隐形中的几个关键问题.逆电磁散射和隐形涂层的研究是很多科技领域的核心,如:雷达、声纳、地理勘探、医疗成像、无线通讯等.由于这些问题具有的特殊结构,严重制约了相关研究的进展.本项目将致力于以下几个问题的研究:1)在规范变化的意义下研究确定实解析类中介电常数、磁导率和电导率三类张量的唯一性;2)建立关于一般电磁散射体定性的唯一性结论;3)在已知目标散射体极少信息的条件下,通过优化测量数据建立一类快速稳定数值重构算法;4)通过正则化思想,利用非奇异的电磁介质设计能达到近似隐形效果的隐形涂层;5)严格地推导隐形实现中可见和不可见的界限,并回答完美隐形是否一定要用奇异材料的问题;6)开发一类有效的数值算法与程序包来研究隐形问题.上述问题在许多领域都能找到重要的应用,本项目的理论和数值方法也可以扩展到电磁学的其它领域中.