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

We consider the 2D inverse conductivity problem for conductivities of the form γ = 1 + χ_Dh 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 I_ω(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.