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

本课题的目的是利用正则牛顿法有效地求解三维逆声和弹声散射问题。这项研究将基于三个基石。本文将对正则牛顿法进行收敛性分析，以建立对该方法的信心，并对正则化参数的选择提供一些启示。为了保证该迭代求解策略的稳定性、快速收敛性和计算效率，将散射场的Frechet导数关于形状参数的表征和有限元撕裂和互连亥姆霍兹（FETI-H）域分解方法扩展到耦合弹声问题。由于远场模式通常仅在有限孔径内测量，因此还将研究重建全孔径数据的两种不同方法。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的一个重要问题。本项目将开发一种有效的反声散射问题的计算方法。所提出的方法对计算科学的基础设施也有很大的潜力。

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.