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Volume 5, Issue 4
A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection

Andreas Karageorghis, Daniel Lesnic & Liviu Marin

Adv. Appl. Math. Mech., 5 (2013), pp. 510-527.

Published online: 2013-08

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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.

  • AMS Subject Headings

65N35, 65N21, 65N38

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-510, author = {Karageorghis , AndreasLesnic , Daniel and Marin , Liviu}, title = {A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.13-13S07}, url = {http://global-sci.org/intro/article_detail/aamm/83.html} }
TY - JOUR T1 - A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection AU - Karageorghis , Andreas AU - Lesnic , Daniel AU - Marin , Liviu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 510 EP - 527 PY - 2013 DA - 2013/08 SN - 5 DO - http://doi.org/10.4208/aamm.13-13S07 UR - https://global-sci.org/intro/article_detail/aamm/83.html KW - Void detection, inverse problem, method of fundamental solutions. AB -

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.

Andreas Karageorghis, Daniel Lesnic & Liviu Marin. (1970). A Moving Pseudo-Boundary MFS for Three-Dimensional Void Detection. Advances in Applied Mathematics and Mechanics. 5 (4). 510-527. doi:10.4208/aamm.13-13S07
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