Open Access
SUMMER 2015 A nonlinear integral equation and an iterative algorithm for an inverse source problem
Rainer Kress, William Rundell
J. Integral Equations Applications 27(2): 179-197 (SUMMER 2015). DOI: 10.1216/JIE-2015-27-2-179


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.


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Rainer Kress. William Rundell. "A nonlinear integral equation and an iterative algorithm for an inverse source problem." J. Integral Equations Applications 27 (2) 179 - 197, SUMMER 2015.


Published: SUMMER 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1323.31006
MathSciNet: MR3395967
Digital Object Identifier: 10.1216/JIE-2015-27-2-179

Primary: 31A25 , 45Q05 , 49N45

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.27 • No. 2 • SUMMER 2015
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