Artificial boundary conditions for axisymmetric eddy current probe problems

Houssem Haddar (1) , Zixian Jiang (1) , Armin Lechleiter (2)

1 DeFI - Shape reconstruction and identification
2 ZeTeM - Zentrum für Technomathematik - Universität Bremen

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 map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as the truncation parameter tends to infinity. Under stronger assumptions on the physical parameters of the eddy current problem, convergence rates are shown. We further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Analyse numérique [cs.NA]

Houssem Haddar, Zixian Jiang, Armin Lechleiter. Artificial boundary conditions for axisymmetric eddy current probe problems. Computers & Mathematics with Applications, 2015, 68 (12, Part A,), pp.1844-1870. ⟨10.1016/j.camwa.2014.10.008⟩. ⟨hal-01072091v2⟩