High Order Numerical Methods for Problems in Electromagetics and Fluid Dynamics

本文概述的提案为我正在进行的计算方法研究计划提供了资金，这些方法适用于电磁学和流体动力学中的工程相关问题。在一个适合研究生研究的项目中，有人提议开发高精度的计算方法来模拟导电光纤光栅的电磁衍射。事实上，模拟材料结构对入射波的电磁响应问题在科学和工程中具有重要意义。该理论在几个研究领域都有应用，包括太阳能研究、光学仪器设计、遥感和通信理论，仅举几例。导电材料在实践中很有趣，因为已知它们在特定情况下在光栅衍射中会产生非常高的吸收，因此在现代太阳能电池的设计中可能是有用的。在另一个项目中，*我们建议研究环形流体环作为基本系统的适用性，以提供卫星绕轴旋转振动的机械阻尼。建议研究环面绕其主对称轴作简谐旋转运动时，环面内产生的流动和壁面剪应力。该项目的目标是确定流体施加在环面上的粘性应力在多大程度上耗散了与振动相关的机械能。有趣的是，这个问题与生物力学中的另一个重要问题有关：弯管中的血液流动。

The proposal outlined in this text provides funding for my ongoing research program in computational methods applied to problems of engineering relevance in electromagnetics and fluid dynamics. In one project suitable for graduate student research, it is proposed to develop highly accurate computational methods to simulate the electromagnetic diffraction from conducting optical gratings. Indeed, the problem of simulating the electromagnetic response of material structures to an incident wave is of great importance in science and engineering. Applications of the theory exist in several fields of study, including solar energy research, optical instrument design, remote sensing, and communications theory, to name a few. Conducting materials are interesting in practice, since they are known to result in remarkably high absorption under particular circumstances in grating diffraction and hence may be useful in the design of modern solar cells. In another project,*we propose to investigate the*suitability of a toroidal fluid ring as basic a system to provide mechanical damping of the rotational oscillations of a satellite about an axis. It is*proposed to study the flow and wall shear stresses which arise in a toroidal geometry when the toroid is subject to harmonic rotational motion*about its principal axis of symmetry. The goal of the project is to determine the degree to which the viscous stresses imposed by the fluid on the*wall of the toroid dissipate the mechanical energy associated with the oscillations. Interestingly this problem is related to another important*problem in biomechanics: blood flow in curved tubes.