Karageorghis, A, Lesnic, D orcid.org/0000-0003-3025-2770 and Marin, L (2018) The method of fundamental solutions for the identification of a scatterer with impedance boundary condition in interior inverse acoustic scattering. Engineering Analysis with Boundary Elements, 92. pp. 218-224. ISSN 0955-7997
Abstract
We employ the method of fundamental solutions (MFS) for detecting a scatterer surrounding a host acoustic homogeneous medium D due to a given point source inside it. On the boundary of the unknown scatterer (assumed to be star-shaped), allowing for the normal velocity to be proportional to the excess pressure, a Robin impedance boundary condition is considered. The coupling Robin function λ may or may not be known. The additional information which is supplied in order to compensate for the lack of knowledge of the boundary ∂D of the interior scatterer D and/or the function λ is given by the measurement of the scattered field (generated by the interior point source) on a curve inside D. These measurements may be contaminated with noise so their inversion requires regularization. This is enforced by minimizing a penalised least-squares functional containing various regularization parameters to be prescribed. In the MFS, the unknown scattered field us is approximated with a linear combination of fundamental solutions of the Helmholtz operator with their singularities excluded from the solution domain D and this yields the discrete version of the objective functional. Physical constraints are added and the resulting constrained minimization problem is solved using the MATLAB© toolbox routine lsqnonlin. Numerical results are presented and discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017, Elsevier Ltd. All rights reserved. This is an author produced version of a paper published in Engineering Analysis with Boundary Elements. Uploaded in accordance with the publisher's self-archiving policy |
Keywords: | Method of fundamental solutions; Interior inverse scattering; Impedance boundary condition; Regularization |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Sep 2017 09:36 |
Last Modified: | 02 Aug 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.enganabound.2017.07.005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120904 |