An iterative method for determining the shape and conductivity of a homogeneous inclusion in the two-dimensional electrical impedance tomography problem

The problem of electrical impedance tomography in a bounded two-dimensional domain with a piecewise two-valued constant electrical conductivity is considered. It is required to determine an unknown boundary between the regions of different conductivities and to obtain the conductivity in one of these regions using the input information on the electric field measured on the outer boundary of the domain. An iterative method for solving this problem is proposed. The corresponding numerical results are discussed.