Linear sampling methods for inverse boundary value problems in potential theory Original Research Article

Linear sampling methods have been recently suggested and developed by Colton and Kirsch for the approximate solution of inverse obstacle scattering problems, i.e., for inverse boundary value problems for the Helmholtz equation. We present an analogue of these methods for the solution of an inverse Neumann problem for the Laplace equation. We will describe both the mathematical foundation and the numerical implementation illustrated through two-dimensional examples.