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

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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.