Virtual Resistive Network Algorithm for Inverse Conductivity Problems ∗

In this paper, we illustrated a numerical algorithm which we refer to as the Virtual Resistive Network algorithm, to reconstruct the interior conductivity from interior current densities. In the algorithm, the essence is to introduce a virtual resistive network onto the continuum domain. The algorithm is noniterative and has certain degrees of flexibility in use. We reconstructed the isotropic conductivity, from one interior current density and known conductivity on partial boundary, and reconstructed the orthotropic conductivity, from two pieces of current densities and known conductivity on partial boundary. Numerically simulated results with noise are presented. Various features of the algorithm against the noise was reported.