Year: 2024
Author: Andreas Karageorghis, Daniel Lesnic, Liviu Marin
Communications in Computational Physics, Vol. 35 (2024), Iss. 3 : pp. 553–578
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 ${\rm MATLAB}^®$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0207
Communications in Computational Physics, Vol. 35 (2024), Iss. 3 : pp. 553–578
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Void detection inverse problem method of fundamental solutions.