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

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

Author Details

Andreas Karageorghis

Daniel Lesnic

Liviu Marin

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