An iterative method for solving a 3D electrical impedance tomography problem in the case of piecewise constant conductivity and several measurements on the boundary

The electrical impedance tomography problem is considered in a bounded three-dimensional domain with a piecewise constant electrical conductivity. The inhomogeneity boundary is assumed to be unknown. The inverse problem is to determine the surface that is the inhomogeneity boundary using several known 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. Some numerical results are discussed.