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Published October 16, 2018 | Published
Journal Article Open

Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes

Abstract

This paper is concerned with time-harmonic acoustic scattering of plane waves in one or two inhomogeneous half-planes with an unbounded interface. The contrast function is supposed to have a compact support, while the infinite interface is a local perturbation of the x_1-axis. For an acoustically impenetrable interface, the scattering phenomenon occurs in one half-plane only and the impedance (Robin) boundary value problem is investigated. In the penetrable case, we study a transmission problem in two half-planes. Our approach for forward scattering is based on the finite element method in a truncated bounded domain coupled with the boundary element method. Numerical experiments are tested to verify our scheme. For the inverse problem, we prove that the near-field data of a finite number of incoming plane waves or a single point source wave uniquely determine the shape of a rectangular cavity of impedance-type.

Additional Information

© 2018 Society for Industrial and Applied Mathematics. Received by the editors January 5, 2018; accepted for publication (in revised form) August 1, 2018; published electronically October 16, 2018. Funding: The first author's work was supported in part by an NSFC Innovative Group Fund (11621101), an Integrated Project of the Major Research Plan of NSFC (91630309), and an NSFC A3 Project (11421110002). The second author's work was supported by the NSFC grant (11671028) and NSAF grant (U1530401). The third author's work was partially supported by the NSFC grant (11501063).

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August 19, 2023
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October 19, 2023