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A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

Published online by Cambridge University Press:  03 June 2015

Andreas Karageorghis ,
Daniel Lesnic  and
Liviu Marin
Andreas Karageorghis*
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Daniel Lesnic*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Liviu Marin*
Affiliation:
Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, P.O.Box 1-863, 010141 Bucharest, and Centre for Continuum Mechanics, Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei, 010014 Bucharest, Romania
*
Corresponding author. Email: andreask@ucy.ac.cy
Email: amt5ld@maths.leeds.ac.uk
Email: marin.liviu@gmail.com
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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.

Keywords

65N3565N2165N38Void detectioninverse problemmethod of fundamental solutions
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Special Issue 4 , August 2013 , pp. 510 - 527
Copyright
Copyright © Global-Science Press 2013

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