Mathematical Sciences: Wave Propagational Inverse Problems in Media with Microstructure

本研究项目是关于微结构介质中波传播反问题的研究。该程序由两部分组成：1)准确、高效地模拟微结构介质中的波动现象；2)求解反问题，以确定介质的微结构特性。研究的主要工具将是同质化方法。我们将进行显式的解析和数值计算，以模拟扰动在几种相关的微结构介质模型中的传播。将对数值格式的精度进行分析。将研究从观察到的介质的瞬变响应来表征介质的微观结构的问题。将考虑几个重要的申请。将分析介质的微观结构细节与其观察到的响应之间的函数关系。这个项目的目标是开发专门用于解决这类反问题的有效的数值格式。

This research project concerns the study of wave propagational inverse problems in media with microstructure. The program has two components: 1) Accurate and efficient modeling of wave phenomena in media with microstructure, and 2) Solution of inverse problems for the determination of microstructural properties of media. The main tool for the study will be the method of homogenization. Explicit analytical and numerical calculations will be carried out to simulate the propagation of disturbances in several relevant models of media with microstructure. Analysis of the accuracy of numerical schemes will be performed. The problem of characterizing the microstructure of a medium from observed transient responses of the medium will be studied. Several important applications will be considered. The functional relationship between the microstructural details of a medium and its observed responses will be analyzed. It is the goal of this project to develop efficient numerical schemes specialized to solving inverse problems of this type.