On rational approximation methods for inverse source problems

Type
Article

Authors
Rundell, William
Hanke, Martin

KAUST Grant Number
KUS-CI-016-04

Online Publication Date
2011-02-23

Print Publication Date
2011

Date
2011-02-23

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 case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.

Citation
Rundell W, Hanke M (2011) On rational approximation methods for inverse source problems. IPI 5: 185–202. Available: http://dx.doi.org/10.3934/ipi.2011.5.185.

Acknowledgements
This research was supported by the National Science Foundation under grant DMS-0715060 and by the King Abdullah University of Science and Technology (KAUST) award KUS-CI-016-04.

Publisher
American Institute of Mathematical Sciences (AIMS)

Journal
Inverse Problems and Imaging

DOI
10.3934/ipi.2011.5.185

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