Numerical Method for Solving an Inverse Problem for Laplace’s Equation in a Domain with an Unknown Inner Boundary

Abstract

An inverse problem for Laplace’s equation in a doubly connected two-dimensional domain is considered. Given Dirichlet and Neumann data specified on the known outer boundary of the domain, the task is to determine an unknown inner boundary on which the function takes a constant value. The uniqueness of the solution to this inverse problem is proved. An iterative numerical method for determining the unknown boundary is proposed. Numerical results are presented.