Nonlinear integral equations and the iterative solution for an inverse boundary value problem
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Determining the shape of a perfectly conducting inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modelled as an inverse boundary value problem for harmonic functions. We present a novel solution method for such inverse boundary value problems via a pair of nonlinear and ill-posed integral equations for the unknown boundary that can be solved by linearization, i.e., by regularized Newton iterations. We present a mathematical foundation of the method and illustrate its feasibility by numerical examples. 2005 IOP Publishing Ltd.
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Kress, Rainer||Rundell, William