Free Surface Fluid Mechanics and Electromagnetic Scattering: Stable, High-Order Perturbation Techniques

摘要0406007，尼科尔斯，圣母大学自由表面流体力学和电磁散射：稳定的，高阶扰动技术的主要研究者（PI）提出的调查ofundamental现象在自由表面理想的流体流动，电磁和声散射。 其中的应用程序是有效的，稳定的，高阶计算的三维，毛细重力水波，和数值调查他们的动态稳定性。 PI将解决的另一个问题是对无界域上的微分方程施加“非反射”边界条件，特别是在电磁和声散射的设置中。 PI还提出了一个综合的两个主要领域的研究，通过研究后向散射返回的电磁辐射从行进的海浪。 在这个项目中的一个统一的元素，和主要的数值工具PI将采用，是一类边界摄动方法首先介绍了O。布鲁诺·F Reitich在声散射和电磁散射问题的数值模拟的背景下. 这些方法随后被Reitich和PI显着改进和稳定，用于计算Dirichlet-Neumann算子的BVP，并近似散射配置。 在这些改进中，PI Reitich开发了“变换场展开”（TFE）方法，该方法能够可靠地、高阶地、稳定地对BVP和FBP进行微扰计算。虽然这种方法在解决竞争方法无法达到的模拟问题方面非常成功，但与其他技术（例如边界积分/元素）相比，它在计算复杂性方面有些不利。 PI提出的最后一个项目是研究这种TFE方法的两个改进，以提高其效率。固定和自由边界问题出现在工程和科学的所有领域。 在这个proposalare经典的自由边界问题的表面waveson一个大的水体（如湖，海，或海洋）的运动，和fixedboundary问题的散射电磁波或声波从一个不规则的表面。 精确可靠的表面波模拟不仅用于模拟开放式海洋结构（例如石油平台）的能力，而且还用于研究污染物和其他环境物质在湖泊，海洋和海洋中的传输。 电磁散射和声散射的应用可以在雷达、成像和传感等领域得到应用。 许多数值技术可用于这些问题的模拟，本提案的目标之一是利用和改进由首席研究员（PI）和合作者发现和改进的一类技术。 特别是，当上述问题在全三维中模拟时，计算变得相当密集，问题真正成为高性能计算的问题。

Abstract 0406007, Nicholls, University of Notre DameFree Surface Fluid Mechanics and Electromagnetic Scattering: Stable, High-Order Perturbation Techniques The Principal Investigator (PI) proposes the investigation offundamental phenomena in free-surface ideal fluid flows, andelectromagnetic and acoustic scattering. Among the applications arethe efficient, stable, high-order computation of travelingthree-dimensional, capillary-gravity water waves, and a numericalinvestigation of their dynamic stability. Another problem the PI willaddress is the imposition of "non-reflecting" boundary conditions fordifferential equations posed on unbounded domains, particularly in thesetting of electromagnetic and acoustic scattering. The PI alsoproposes a synthesis of two major areas of his research through thestudy of backscattering returns of electromagnetic radiation fromtraveling ocean waves. A unifying element in this project, and theprincipal numerical tool the PI will employ, is a class of boundaryperturbation methods first introduced by O. Bruno & F. Reitich in thecontext of numerical simulation of acoustic and electromagneticscattering problems. These methods have subsequently beensignificantly refined and stabilized by Reitich and the PI for the BVPof computing Dirichlet-Neumann operators, and approximating scatteringconfigurations. Among these refinements, the PI & Reitich developedthe method of "Transformed Field Expansions" (TFE) which enables thereliable, high-order, stable perturbative computation of BVP and FBP.While this method is extremely successful in resolving simulationswell outside the reach of competing methods, it is somewhatdisadvantaged in terms of computational complexity in comparison toother techniques (e.g. boundary integrals/elements). A final projectthat the PI proposes is the investigation of two refinements of thisTFE approach to increase its efficiency.Fixed and free boundary problems arise in all areas of engineering andthe sciences. Two particular instances of relevance in this proposalare the classic free boundary problem of the motion of surface waveson a large body of water (e.g. a lake, sea, or ocean), and the fixedboundary problem of scattering of electromagnetic or acoustic wavesfrom an irregular surface. The accurate and reliable simulation ofsurface waves is used not only to model the capabilities of open-oceanstructures (e.g. oil platforms), but also in the study of transport ofpollutants and other substances of environmental interest acrosslakes, seas, and oceans. Applications of electromagnetic and acousticscattering come in problems of radar, imaging, and sensing to namejust a few. Many numerical techniques are available for thesimulation of these problems and one of the goals of this proposal isthe utilization and improvement of a class of techniques discoveredand refined by the Principal Investigator (PI) and collaborators. Inparticular, when the problems mentioned above are simulated in fullthree dimensions, the computations become quite intensive and theissues truly become those of high-performance computing.