Iterative method for solving a three-dimensional electrical impedance tomography problem in the case of piecewise constant conductivity and one measurement on the boundary

The problem of electrical impedance tomography in a bounded three-dimensional domain with a piecewise constant electrical conductivity is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem is to determine the surface that is the boundary of the inhomogeneity from given measurements of the potential and its normal derivative on the outer boundary of the domain. An iterative method for solving the inverse problem is proposed, and numerical results are presented.