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The Method of Fundamental Solutions for Direct Cavity Problems in EIT

Borman, DJ, Ingham, DB, Johansson, T and Lesnic, D (2007) The Method of Fundamental Solutions for Direct Cavity Problems in EIT. In: Trevelyan, J, (ed.) Advances in Boundary Integral Methods-Proceedings of 6th UK conference on Boundary Integral Methods (proceedings). Advances in Boundary Integral Methods-Proceedings of 6th UK conference on Boundary Integral Methods, Durham. Durham Publications , 193 - 202 . ISBN 978-0-9535558-3-3

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Abstract

The Method of Fundamental Solutions (MFS) is an effective technique for solving linear elliptic partial differential equations, such as the Laplace and Helmholtz equation. It is a form of indirect boundary integral equation method and a technique that uses boundary collocation or boundary fitting. In this paper the MFS is implemented to solve A numerically an inverse problem which consists of finding an unknown cavity within a region of interest based on given boundary Cauchy data. A range of examples are used to demonstrate that the technique is very effective at locating cavities in two-dimensional geometries for exact input data. The technique is then developed to include a regularisation parameter that enables cavities to be located accurately and stably even for noisy input data.

Item Type: Proceedings Paper
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Process, Environmental and Materials Engineering (Leeds) > Centre for Computational Fluid Dynamics (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 23 Feb 2012 15:34
Last Modified: 08 Feb 2013 17:37
Status: Published
Publisher: Durham Publications
URI: http://eprints.whiterose.ac.uk/id/eprint/43699

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