Mathematical Sciences: Wave Propagational Inverse Problems in Media with Microstructure

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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.