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

abstract

• 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.

authors

• Rundell, William

published proceedings

• INVERSE PROBLEMS

author list (cited authors)

• Kress, R., & Rundell, W.

citation count

• 127

complete list of authors

• Kress, R||Rundell, W

publication date

• August 2005

publisher

• IOP Publishing  Publisher

published in

• Inverse Problems  Journal

keywords

• 49 Mathematical Sciences
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1088/0266-5611/21/4/002

start page

• 1207

end page

• 1223

volume

• 21

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1088%2F0266-5611%2F21%2F4%2F002