Nonlinear integral equations and the iterative solution for an inverse boundary value problem

By Rainer Kress, William Rundell. 2005

173 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/87a58fb42447bc0f6da3e3a155f2fe3d59841b97

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In Biomedical Engineering

In Electrical and Electronic Engineering

In Mathematical Physics

Citations in the corpus

A quasi-reversibility approach to solve the inverse obstacle problem (2010, methodology): “Among all articles based on such methods, the specific case of the obstacle characterized by a homogeneous Dirichlet data is addressed in [14] and in [15, 16].”
Reconstruction of a moving boundary from Cauchy data in one-dimensional heat equation (2009, background): “Reconstruction of a corroded boundary from the Laplace equation has been investigated in some papers [1, 2, 4, 8, 10, 20, 27, 30, 37, 38].”
Integral equations for inverse problems in corrosion detection from partial Cauchy data (2007, methodology): “This method has been recently suggested by Kress and Rundell [17] to determine the shape of a perfectly conducting obstacle in a homogeneous background from overdetermined Cauchy data.”