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

Abstract

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 Nyström-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.

arXiv admin note: text overlap with arXiv:1811.12579

References in corpus (12)

• Phase Retrieval with Application to Optical Imaging
• Recovering scattering obstacles by multi-frequency phaseless far-field data
• Retrieval of acoustic sources from multi-frequency phaseless data
• Recovering an electromagnetic obstacle by a few phaseless backscattering measurements
• Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency
• Inverse elastic scattering problems with phaseless far field data
• A Fast Solver for the Elastic Scattering of Multiple Particles
• Uniqueness in inverse cavity scattering problems with phaseless near-field data
• Uniqueness in phaseless inverse scattering problems with superposition of incident point sources
• Phased and phaseless domain reconstruction in inverse scattering problem via scattering coefficients
• Uniqueness in inverse acoustic scattering with phaseless near-field measurements
• Uniqueness in inverse scattering problems with phaseless far-field data at a fixed frequency. II

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• A highly accurate boundary integral method for the elastic obstacle scattering problem