High-order boundary perturbation methods for the solution of problems of wave propagation

本项目致力于研究复杂物体和材料对电磁辐射的响应。特别是，在解决障碍物和界面散射的经典问题时，理论和计算都取得了进展。这种进展将源于基于高阶摄动和解析延拓技术的这些问题的新方法的进一步发展，这种方法以前由首席调查员(PI)介绍，并已被证明在各种构型下都能提供非常准确的结果。将开展的调查涉及分析和可能改进产生这些高精度计算的每一个要素，特别是它们对所产生的数字代码的适用性和准确性的影响。在宏观物体电磁返回的同时，PI将致力于加强他最近设计的算法，通过纳入各种非线性流体动力学和电磁效应来模拟导电和/或磁性渗透的微观颗粒悬浮液。电磁辐射的产生、控制和检测一直是、并将继续是从雷达和断层扫描到光学系统、通信和“智能”材料等领域的无数工程和技术进步的核心。从历史上看，这些进步中的大多数都是由更多的直觉和物理洞察力引导的扩张性实验，而不是数学建模和计算。最近，随着计算机变得更加强大，尝试将它们纳入设计过程变得很自然，寻找快速、准确和可靠的算法来数值求解复杂的模型成为科学的中心问题之一。该项目围绕着这一搜索，寻求增强目前可用来确定大型物体和微观复合分散体的电磁特征的技术。预计将在这里开发的方法将产生直接影响的特定应用领域包括目标识别和先进可控(电磁和磁流变)流体的设计。

This project is concerned with the study of the response of complex objects and materials to electromagnetic radiation. In particular, theoretical and computational advances are projected in the solution of classical problems of wave scattering by obstacles and interfaces. Such progress will stem from the further development of a new approach to these problems, based on high-order perturbation and analytic continuation techniques, that was previously introduced by the principal investigator (PI) and which has been proved to deliver very accurateresults for a variety of configurations. The investigations to be carried out relate to the analysis and possible improvement of each of the elements that combined to produce these highly precise calculations and, in particular, with their influence on the applicability and accuracy of the resulting numerical codes. Concurrent with this effort on the electromagnetic return of macroscopic objects, the PI will work to enhance his recently devised algorithms for the simulation of electrically conducting and/or magnetically permeable microscopic particulate suspensions, by incorporating a variety of nonlinear hydrodynamic and electromagnetic effects.The generation, control and detection of electromagnetic radiation hasbeen, and continues to be, at the core of innumerable engineering and technological advances in areas ranging from radar and tomography to optical systems, communications and "smart" materials. Historically, most of these advances have resulted from expansive experimentation guided more by intuition and physical insight than by mathematical modeling and computations. Recently, as computers grew more powerful, it became natural to attempt to incorporate them into design processes, and the search for fast, accurate and reliable algorithms to numerically solve sophisticated models turned into one of science's central problems.This project revolves around this search as it seeks to enhance currently available techniques for the determination of the electromagnetic signatures of large objects and microscopic composite dispersions. Particular areas of application where the methods to be developed here are expected to have a direct impact include target recognition and the design of advanced controllable (electro and magnetorheological) fluids.