Karageorghis, A and Lesnic, D (2018) Reconstruction of an elliptical inclusion in the inverse conductivity problem. International Journal of Mechanical Sciences, 142-3. pp. 603-609. ISSN 0020-7403
Abstract
This study reports on a numerical investigation into the open problem of the unique reconstruction of an elliptical inclusion in the potential field from a single set of nontrivial Cauchy data. The investigation is based on approximating the potential fields of a composite material as a linear combination of fundamental solutions for the Laplace equation with sources shifted outside the solution domain and its boundary. The coefficients of these finite linear combinations are unknown along with the centre, the lengths of the semi-axes and the orientation of the sought ellipse. These are determined by minimizing the least-squares objective functional describing the gap between the given and computed data. The extension of the proposed technique for the reconstruction of two ellipses is also considered.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2018 Elsevier Ltd. All rights reserved. This is an author produced version of a paper published in International Journal of Mechanical Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Elliptical inclusion; Inverse conductivity problem; Method of fundamental solutions |
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: | 04 May 2018 11:31 |
Last Modified: | 10 May 2019 00:43 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ijmecsci.2018.05.002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:130417 |