The method of fundamental solutions for the inverse conductivity problem

Abstract

In this article, we propose a simple method for detecting an inclusion Ω2 embedded in a host electrostatic medium Ω1 from a single Cauchy pair of voltage and current flux measurements on the exterior boundary of Ω1. A nonlinear constrained minimization regularized method of fundamental solutions is developed for the numerical solution of this inverse problem. The stability of the numerical scheme is investigated by inverting measurements contaminated by random noise. © 2010 Taylor & Francis.