At the interface between semiclassical analysis and numerical analysis of wave propagation problems

波传播问题的半经典分析和数值分析之间的接口

• 批准号: EP/R005591/1
• 负责人: Euan Spence
• 金额: $ 130.88万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FR005591%2F1
• 关键词: interface; between; semiclassical; analysis; numerical

Our understanding of wave propagation underpins several important technologies in everyday use. For example, WiFi and mobile phones use electromagnetic waves to transmit information, and the technologies in seismic and medical imaging use acoustic, elastic, and electromagnetic waves to obtain information about the ocean floor and the human body. Over the last few years, the investigator has worked with, on the one hand, researchers interested in wave phenomena from a purely mathematical point of view (without any thought of applications), and, on the other hand, researchers interested primarily in improving how wave phenomena are simulated in applications (with this understanding then feeding into new technologies). This experience has uncovered huge untapped potential in the relationship between the theoretical aspects of wave propagation and the more-practical aspects, and this fellowship seeks to exploit this.The overall goals are to (i) prove fundamental theoretical results about wave propagation, motivated by applications, and (ii) use these theoretical results to prove fundamental results about how wave propagation is simulated using computers, addressing long-standing open problems and developing new numerical methods that have the potential to change the technologies used in the huge variety of practical applications of wave propagation.

我们对波传播的理解是日常使用中的几种重要技术。例如，WiFi和手机使用电磁波传输信息，地震和医学成像中的技术使用声学，弹性和电磁波来获取有关海底和人体的信息。在过去的几年中，研究人员从纯粹的数学角度（没有任何应用程序）中与对波浪现象感兴趣的研究人员合作，另一方面，研究人员主要有兴趣改善如何改善如何改善在应用中模拟了波浪现象（随着这种理解，然后以新技术为食）。这种体验已经揭示了波传播的理论方面与更实用的方面之间关系的巨大尚未开发的潜力，并且该奖学金旨在利用这一点。总体目标是（i）证明波动传播的基本理论结果，由此激励。应用程序，以及（ii）使用这些理论结果来证明如何使用计算机模拟波传播，解决长期存在的开放问题并开发新的数值方法，这些方法有可能更改在各种实际应用中使用的技术波传播。

项目成果

Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains

• DOI: 10.1007/s00211-021-01256-x
• 发表时间: 2021-05
• 期刊: Numerische Mathematik
• 影响因子: 2.1
• 作者: S. Chandler-Wilde;E. Spence

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

• DOI: 10.1090/mcom/3447
• 发表时间: 2017-11
• 期刊: Math. Comput.
• 作者: M. Bonazzoli;V. Dolean;I. Graham;E. Spence;Pierre-Henri Tournier

Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains

• DOI: 10.48550/arxiv.2210.02432
• 发表时间: 2022-10
• 期刊: ArXiv
• 作者: S. Chandler-Wilde;E. Spence

Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?

• DOI: 10.1016/j.cam.2018.11.035
• 发表时间: 2018-06
• 期刊: J. Comput. Appl. Math.
• 作者: G. Diwan;A. Moiola;E. Spence

High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis

抛物线捕获下亥姆霍兹方程的高频界及其在数值分析中的应用

• DOI: 10.1137/18m1234916
• 发表时间: 2020
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Chandler-Wilde S