Journal of Integral Equations and Applications

A nonlinear integral equation and an iterative algorithm for an inverse source problem

Rainer Kress and William Rundell

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Abstract

We consider the inverse problem of recovering the shape of an extended source of known homogeneous strength within a conducting medium from one voltage and current measurement on the accessible boundary of the medium and present an iterative solution method via boundary integral equations. The main idea of our approach is to equivalently reformulate the inverse source problem as an inverse boundary value problem with a non-local Robin condition on the boundary of the source domain. Following our approach in \cite{KR} for an inverse Dirichlet problem, from Green's representation formula we obtain a nonlinear integral equation for the unknown boundary curve which can be solved by regularized Newton iterations. We present the foundations of the inverse algorithm and illustrate its feasibility by some numerical examples.

Article information

Source
J. Integral Equations Applications, Volume 27, Number 2 (2015), 179-197.

Dates
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1441790285

Digital Object Identifier
doi:10.1216/JIE-2015-27-2-179

Mathematical Reviews number (MathSciNet)
MR3395967

Zentralblatt MATH identifier
1323.31006

Subjects
Primary: 31A25: Boundary value and inverse problems 45Q05: Inverse problems 49N45: Inverse problems

Citation

Kress, Rainer; Rundell, William. A nonlinear integral equation and an iterative algorithm for an inverse source problem. J. Integral Equations Applications 27 (2015), no. 2, 179--197. doi:10.1216/JIE-2015-27-2-179. https://projecteuclid.org/euclid.jiea/1441790285


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