High Order Numerical Methods for Problems in Electromagetics and Fluid Dynamics

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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.