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The Method of Fundamental Solutions for Direct Cavity Problems in EIT

By DJ Borman, DB Ingham, T Johansson and D Lesnic

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

Publisher: J. Trevelyan
Year: 2007
OAI identifier: oai:eprints.whiterose.ac.uk:42783

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