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，高阶微扰技术首席研究员(PI)提出了研究自由表面理想流体流动的基本现象，以及电磁和声散射。其中的应用包括对三维毛细重力水波的高效、稳定、高阶计算，以及对其动态稳定性的数值研究。PI将解决的另一个问题是对无界区域上提出的微分方程组施加“非反射”边界条件，特别是在电磁和声波散射的集合中。PI还通过研究传播的海浪的电磁辐射的后向散射回波，提出了他研究的两个主要领域的综合。在这个项目中的一个统一元素，也是PI将使用的主要数值工具，是一类边界摄动方法，首先由O.Bruno和Amp；F.Reitich在声学和电磁散射问题的数值模拟中引入。这些方法随后被Reitich和PI显著改进和稳定，用于计算Dirichlet-Neumann算子和近似散射组态的BVP。在这些改进中，PI和Amp；Reitich发展了“变换场展开”(TFE)方法，它使得BVP和FBP的稳定、高阶、稳定的微扰计算成为可能。虽然这种方法在解决竞争方法无法解决的模拟问题方面非常成功，但与其他技术(例如边界积分/单元)相比，它在计算复杂性方面存在一些劣势。PI提出的最后一个项目是调查这种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所有工程和科学领域。这一建议中涉及的两个具体实例是：大水域(如湖泊、海洋或海洋)表面波运动的经典自由边界问题，以及从不规则表面散射的电磁波或声波的固定边界问题。准确可靠的表面波模拟不仅用于模拟开放海洋结构物(如石油平台)的能力，而且还用于研究污染物和其他与环境有关的物质在湖泊、海洋和海洋之间的传输。电磁和声散射的应用涉及雷达、成像和传感等问题，仅举几例。有许多数值技术可以用来模拟这些问题，本方案的目的之一是利用和改进由首席调查员(PI)和合作者发现和改进的一类技术。特别是，当上述问题被全三维模拟时，计算变得相当密集，问题真正变成了高性能计算的问题。

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.