Artificial boundary conditions for axisymmetric eddy current probe problems

We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann (DtN) map is proposed and mathematically justified via the analysis of a nonselfadjoint spectral problem. We rely of results from the spectral theory of compact perturbations of selfadjoint operators. Convergence for truncated DtN map is also analyzed. We validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes.