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The reconstruction of sources and inclusions by rational approximation

Presented by: 
W Rundell
Date: 
Tuesday 25th October 2011 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the elliptic case. In particular we consider steady-state electrostatic or thermal imaging and giving boundary value problems for Laplace's equation or the case of inverse scattering and near/far field data for the Helmholtz equation. Our inclusions can be interior forces with compact support or obstacles with a fixed, given boundray condition although we shall concentrate on the former situation. We propose a series of algorithms that under certain assumptions allows for the determination of the support set by solving a simpler ``equivalent point source'' problem.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons