Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements

Abstract

We consider the 2D inverse conductivity problem for conductivities of the form γ = 1 + χDh defined in a bounded domain Ω⊂2 with C∞ boundary ∂Ω. Here D⊂Ω and h∊L∞(D) are such that γ has a jump along ∂D. It was shown by Ikehata (Ikehata M J. Inverse and Ill-Posed Problems at press) that the Dirichlet-Neumann map determines the indicator function Iω(τ,t) that can be used to find the convex hull of D. In this paper we find numerically the indicator function for examples with constant h and recover the convex hull of D.