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

基本信息

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

项目摘要

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观点（没有任何对应用的想法）开始对波浪现象感兴趣的研究人员，另一方面，另一方面，研究人员，研究人员主要有兴趣改善如何在应用中模拟波浪现象的方式（并以这种理解为新技术，这是对波浪现象的模拟方式）。这种经验已经发现了波浪传播的理论方面与更实用的方面之间关系的巨大潜力，并且该奖学金试图利用这一点。总体目标是（i）（i）证明对波浪传播的基本理论结果，通过应用程序的发展，以及ii的基本计算结果，以解决波动的发展，以及ii仿真的基础，（ii）是仿真的，（ii）仿真的基本结果是对波浪传播的发展。具有更改波传播的各种实际应用中使用的技术的潜力的数值方法。