An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the location and shape of the elastic obstacle by using either t...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Dong, Heping, Lai, Jun, Li, Peijun
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 10.07.2019
Subjects:
Acoustics
Boundary integral method
Boundary value problems
Elastic scattering
Far fields
Helmholtz equations
Integral equations
Inverse problems
Nonlinear equations
Numerical analysis
Numerical methods
Plane waves
Robustness (mathematics)
Well posed problems
ISSN:2331-8422
Online Access:Get full text
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Summary:Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the location and shape of the elastic obstacle by using either the phased or phaseless far-field data. By introducing the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem of the Helmholtz equations. The jump relations are studied for the second derivatives of the single-layer potential in order to establish the corresponding boundary integral equations. The well-posedness is discussed for the solution of the coupled boundary integral equations. An efficient and high order Nystr\"{o}m-type discretization method is proposed for the integral system. A numerical method of nonlinear integral equations is developed for the inverse problem. For the case of phaseless data, we show that the modulus of the far-field pattern is invariant under a translation of the obstacle. To break the translation invariance, an elastic reference ball technique is introduced. We prove that the inverse problem with phaseless far-field pattern has a unique solution under certain conditions. In addition, a numerical method of the reference ball technique based nonlinear integral equations is also proposed for the phaseless inverse problem. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed methods.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1907.05249