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Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes

Bao, Gang and Hu, Guanghui and Yin, Tao (2018) Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes. SIAM Journal on Applied Mathematics, 78 (5). pp. 2672-2691. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:20181126-094655744

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/18M1164068DOIArticle
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).
Funders:
Funding AgencyGrant Number
Natural National Science Foundation of China11621101
Natural National Science Foundation of China91630309
Natural National Science Foundation of China11421110002
Natural National Science Foundation of China11671028
National Natural Science Foundation of ChinaU1530401
National Natural Science Foundation of China11501063
Subject Keywords:acoustic scattering, locally perturbed half-planes, coupled method, inverse scattering, uniqueness
Classification Code:AMS subject classifications. 35C15, 65N21, 65N30, 65N38
Record Number:CaltechAUTHORS:20181126-094655744
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181126-094655744
Official Citation:Time-Harmonic Acoustic Scattering from Locally Perturbed Half-Planes. Gang Bao, Guanghui Hu, and Tao Yin. SIAM Journal on Applied Mathematics 2018 78:5, 2672-2691
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91157
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Nov 2018 17:56
Last Modified:26 Nov 2018 17:56

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