TY - JOUR

T1 - On rational approximation methods for inverse source problems

AU - Rundell, William

AU - Hanke, Martin

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011/2/23

Y1 - 2011/2/23

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/599043

UR - http://aimsciences.org//article/doi/10.3934/ipi.2011.5.185

UR - http://www.scopus.com/inward/record.url?scp=79951733714&partnerID=8YFLogxK

U2 - 10.3934/ipi.2011.5.185

DO - 10.3934/ipi.2011.5.185

M3 - Article

VL - 5

SP - 185

EP - 202

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 1

ER -