A moving pseudo-boundary method of fundamental solutions for void detection

We propose a new moving pseudo‐boundary method of fundamental solutions (MFS) for the determination of the boundary of a void. This problem can be modeled as an inverse boundary value problem for harmonic functions. The algorithm for imaging the interior of the medium also makes use of radial polar...

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Bibliographic Details
Published in:Numerical methods for partial differential equations Vol. 29; no. 3; pp. 935 - 960
Main Authors: Karageorghis, Andreas, Lesnic, Daniel, Marin, Liviu
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.05.2013
Wiley Subscription Services, Inc
Subjects:
Algorithms
Imaging
inverse problem
Inverse problems
Mathematical models
method of fundamental solutions
Nonlinearity
Numerical analysis
Parametrization
void detection
Voids
ISSN:0749-159X, 1098-2426
Online Access:Get full text
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Summary:We propose a new moving pseudo‐boundary method of fundamental solutions (MFS) for the determination of the boundary of a void. This problem can be modeled as an inverse boundary value problem for harmonic functions. The algorithm for imaging the interior of the medium also makes use of radial polar parametrization of the unknown void shape in two dimensions. The center of this radial polar parametrization is considered to be unknown. We also include the contraction and dilation factors to be part of the unknowns in the resulting nonlinear least‐squares problem. This approach addresses the major problem of locating the pseudo‐boundary in the MFS in a natural way, because the inverse problem in question is nonlinear anyway. The feasibility of this new method is illustrated by several numerical examples. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
Bibliography:Romanian National Authority for Scientific Research
istex:3E090EC1096A693CC32CC3220A08AE75BC320E50
ArticleID:NUM21739
CNCS-UEFISCDI - No. PN-II-ID-PCE-2011-3-0521
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SourceType-Scholarly Journals-1
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.21739