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

自由表面流体力学和电磁散射：稳定的高阶扰动技术

• 批准号: 0537511
• 负责人: David Nicholls
• 金额: --
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0537511&HistoricalAwards=false
• 关键词: Free; Surface; Fluid; Mechanics; Electromagnetic

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.

摘要0406007，Noicholls，Notre University University University of Notre damefore Surface机械和电磁散射：稳定，高阶扰动技术主要研究者（PI）提出了在自由表面上的无汇率现象的研究，理想流体，理想流体，andectromagnetic andectromagnetic and声音散射。 在这些应用中，有效，稳定，高阶计算的毛细血管毛细管水波和其动态稳定性的数值进行了数值。 PI WillAddress的另一个问题是强加了“不反射”边界条件伪造的方程，该方程在无界域上构成，尤其是在电磁和声学散射的情况下。 pi alsoposes通过traveraver的海浪中电磁辐射的反向散射回报来综合其研究的两个主要领域。 该项目中的一个统一元素，以及PI将要使用的原理数值工具，是O. Bruno＆F。Reitich在声学和电磁播放问题的数值模拟中首先引入的一类边界扰动方法。 这些方法随后通过Reitich和PI进行了良好的细化和稳定，用于BVPOF计算Dirichlet-Neumann运算符，并近似散射configuration。 在这些改进中，Pi＆Reitich开发了“转化现场扩展”（TFE）的方法，该方法可实现BVP和FBP的可靠，高阶，稳定的扰动计算。虽然此方法在将模拟在竞争方法的范围之外解决仿真方面非常成功，与其他技术相比（例如边界积分/元素）相比，它在计算复杂性方面有些偏爱。 PI提出的最终项目是对提高其效率的两种改进的调查。 在此提案中，两个特殊相关的情况是表面波的运动的经典自由边界问题（例如，湖泊，海洋或海洋）以及电磁波或声波散射从不规则表面散射的固定问题。 精确且可靠的表面波的模拟不仅用于对开放式结构（例如油平台）的功能进行建模，还用于研究跨湖，海洋和海洋的Plospolutants和其他环境兴趣的运输。 电磁和声学隔离的应用出现在雷达，成像和感知的问题中，以命名一些。 许多数值技术可用于这些问题的仿真，该提案的目标之一是利用和改进了首席研究员（PI）和合作者所发现的一类技术的利用和改进。 在围栏中，当上述问题在全三个维度上模拟时，计算变得非常密集，而Theissues确实成为了高性能计算的计算。