Year: 2013
Author: Andreas Karageorghis, Daniel Lesnic, Liviu Marin
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 510–527
Abstract
We propose a new moving pseudo-boundary method of fundamental solutions (MFS) for the determination of the boundary of a three-dimensional void (rigid inclusion or cavity) within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary. The algorithm for imaging the interior of the medium also makes use of radial spherical parametrization of the unknown star-shaped void and its centre in three dimensions. We also include the contraction and dilation factors in selecting the fictitious surfaces where the MFS sources are to be positioned in the set of unknowns in the resulting regularized nonlinear least-squares minimization. The feasibility of this new method is illustrated in several numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.13-13S07
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 4 : pp. 510–527
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Void detection inverse problem method of fundamental solutions.