Computational Methods for the Solution of Three-Dimensiional Inverse Acoustic and Elastoacoustic Scattering Problems

本项目的目标是通过正则化牛顿法有效地求解三维声学和弹性声学散射问题。这项研究将基于三个基石。通过对正则化牛顿法的收敛分析，建立了正则化牛顿法的可信度，并对正则化参数的选取有一定的指导意义。为了保证迭代求解策略的稳定性、快速收敛和计算效率，将散射场的Frechet导数关于形状参数的刻画和有限元撕裂互连Helmholtz(FETI-H)区域分解方法推广到求解耦合弹声问题。在声纳、雷达、地球物理勘探、医学成像和无损检测等许多技术中，根据障碍物对已知声波或电磁波的影响来确定障碍物的形状是一个重要的问题。该项目将为声散射反问题提供一种有效的计算方法。拟议的方法还具有极大的潜力，可以使计算科学的基础设施受益。

The objective of this project is to enable an efficient solution by a regularized Newton method of three-dimensional inverse acoustic and elastoacoustic scattering problems. The research will be based upon three cornerstones. The convergence analysis of the regularized Newton method will be performed to establish confidence in this approach and shed some light on the selection of the regularization parameter. In order to ensure the stability, fast convergence, and computational efficiency of this iterative solution strategy, the characterization of the Frechet derivatives of the scattered field with respect to the shape parameters and the Finite Element Tearing and Interconnecting Helmholtz (FETI-H) domain decomposition method will be extended to address coupled elastoacoustic problems. Since the far-field pattern is in general measured only in a limited aperture, two different approaches for reconstructing the full aperture data will also be investigated.The determination of the shape of an obstacle from its effects on known acoustic or electromagnetic waves is an important problem in many technologies such as sonar, radar, geophysical exploration, medical imaging and nondestructive testing. This project will develop an efficient computational method for the inverse acoustic scattering problem. The proposed methodologies also have a great potential for benefiting the infrastructure of computational sciences.