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

本计画的目标是利用正规化牛顿法，有效地求解三维逆声波与弹性声波散射问题。这项研究将基于三个基石。 正则化牛顿法的收敛性分析将被执行，以建立这种方法的信心，并揭示了一些正则化参数的选择。为了确保这种迭代求解策略的稳定性，快速收敛和计算效率，散射场的Frechet导数相对于形状参数和有限元撕裂和互连亥姆霍兹（FETI-H）区域分解方法的表征将扩展到解决耦合弹性声学问题。由于远场模式通常只能在有限孔径内测量，因此还将研究两种不同的方法来重建全孔径数据。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。本计画将发展一种有效的计算方法来求解逆声散射问题。所提出的方法也有很大的潜力，有利于计算科学的基础设施。

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.