Nonlinear integral equations and the iterative solution for an inverse boundary value problem Academic Article uri icon

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.

author list (cited authors)

  • Kress, R., & Rundell, W.

citation count

  • 119

publication date

  • May 2005