### The reconstruction of sources and inclusions by rational approximation

Rundell, W

Tuesday 25 October 2011, 14:00-15:00

Seminar Room 2, Newton Institute Gatehouse

#### 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.

#### Presentation

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