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BOUNDARY INTEGRAL EQUATION METHODS FOR HIGH FREQUENCY SCATTERING PROBLEMS

高频散射问题的边界积分方程法

基本信息

批准号：
EP/F06795X/1
负责人：
Ivan Graham
金额：
$ 36.65万
依托单位：
University of Bath
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2009
资助国家：
英国
起止时间：
2009 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF06795X%2F1
关键词：
BOUNDARY INTEGRAL EQUATION METHODS FREQUENCY

项目摘要

This project concerns the invention, analysis and implementation of new numerical methods for computationally simulating high frequency wave scattering problems. These problems have diverse applications, for example in modelling radar, sonar, acoustic noise barriers, medical ultrasound, and scattering of radiation by atmospheric particles. Our research is supported by four industrial/research organisations who comprise a steering committee and will provide motivating physical applications for the project.The chief technological difficulty which we face in the project is that of computing accurately wave solutions which are highly oscillatory (i.e. varying very quickly). Standard approximation techniques usually break the domain of the problem up into small ''elements'', and use simple (e.g. polynomial) approximations on each element. Then it is known that about 5-10 elements are required in each wavelength to achieve acceptable accuracy, and so the computational work required grows at least in proportion to the frequency of the wave (and often faster than this). In this sense the methods are termed ''not robust'' as frequency increases.We are going to devise, analyse and implement new robust methods for which the cost to obtain a fixed accuracy is bounded (or at worst grows very slowly) as the frequency increases. The programme involves solving problems not only of approximation of highly oscillatory solutions, but also (and this is often harder) analysing the stability and conditioning (i.e. sensitivity ) of the equations which govern them.The chief device which we will use to achieve our objective is the great body of asymptotic techniques for high frequency wave phenomena, some of which which are well-known in the mathematics and physics communities but which have so far been very little used in numerical computation. Part of our project will involve the derivation of new asymptotic analyses and putting them in a form suitable for use in numerical analysis. Scattering problems will be reformulated in such a way that high frequency parts of the solution are handled explicitly (and thus exactly), leaving only the approximation of low frequency components which can be done with low cost. This approach leads to new, challenging and deep problems in consistency, stability, conditioning and numerical integration which must be solved before the robustness of the methods can be rigorously determined. Some of the problems which we face require applying technology which we know will work because of our earlier studies; others require a significant element of risk and a spirit of adventure.The project will involve four investigators and two PDRAs, one involved primarily in analysis and one primarily in scientific computation. Both will also work on applications of relevance to our collaborators.

本计画系关于高频波散射问题之新数值模拟方法之发明、分析与实施。这些问题有不同的应用，例如在建模雷达，声纳，声噪声屏障，医疗超声，和大气颗粒的辐射散射。我们的研究得到四个工业/研究机构的支持，他们组成了一个指导委员会，并将为该项目提供激励性的物理应用。我们在该项目中面临的主要技术困难是精确计算高度振荡（即变化非常快）的波解。标准近似技术通常将问题的域分解为小的“元素”，并对每个元素使用简单的（例如多项式）近似。然后，已知每个波长需要大约5-10个元素才能达到可接受的精度，因此所需的计算工作至少与波的频率成比例地增长（并且通常比这更快）。在这个意义上的方法被称为“不鲁棒”的频率increases.We要设计，分析和实现新的鲁棒方法，获得一个固定的精度的成本是有界的（或在最坏的情况下增长非常缓慢），随着频率的增加。该方案不仅涉及解决问题的近似高度振荡的解决方案，但也（这通常更难）分析稳定性和条件反射（即灵敏度）的方程，支配他们。我们将使用的主要设备，以实现我们的目标是伟大的机构的渐近技术的高频波现象，其中一些在数学和物理界是众所周知的，但迄今为止很少用于数值计算。我们的项目的一部分将涉及新的渐近分析的推导，并把它们以适合于数值分析的形式。散射问题将被重新公式化，以这样一种方式，解决方案的高频部分被显式处理（因此是准确的），只留下低频分量的近似值，可以用低成本完成。这种方法导致新的，具有挑战性的和深层次的问题，在一致性，稳定性，条件和数值积分，必须解决之前的方法的鲁棒性可以严格确定。我们面临的一些问题需要应用我们知道会工作的技术，因为我们以前的研究;其他人需要一个重大的风险因素和冒险精神，该项目将涉及四名调查员和两名PDRA，一名主要从事分析，一名主要从事科学计算。双方还将致力于与我们的合作者相关的应用程序。