Karageorghis, A., Lesnic, D. orcid.org/0000-0003-3025-2770 and Marin, L. (2024) Solution of Inverse Geometric Problems Using a Non-Iterative MFS. Communications in Computational Physics, 35 (3). pp. 553-578. ISSN 1815-2406
Abstract
In most of the method of fundamental solutions (MFS) approaches employed so far for the solution of inverse geometric problems, the MFS implementation typically leads to non-linear systems which were solved by standard nonlinear iterative least squares software. In the current approach, we apply a three-step non-iterative MFS technique for identifying a rigid inclusion from internal data measurements, which consists of: (i) a direct problem to calculate the solution at the set of measurement points, (ii) the solution of an ill-posed linear problem to determine the solution on a known virtual boundary and (iii) the solution of a direct problem in the virtual domain which leads to the identification of the unknown curve using the MATLAB® functions contour in 2D and isosurface in 3D. The results of several numerical experiments for steady-state heat conduction and linear elasticity in two and three dimensions are presented and analyzed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Global Science Press, 2024. This is an author produced version of an article published in Communications in Computational Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Void detection, inverse 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: | 10 Jan 2024 10:32 |
Last Modified: | 16 Apr 2024 14:56 |
Status: | Published |
Publisher: | Global Science Press |
Identification Number: | 10.4208/cicp.OA-2023-0207 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207014 |
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