Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains

Mohamed Jaoua (1) , Juliette Leblond (2) , Moncef Mahjoub (3) , Jonathan Partington (4)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 APICS - Analysis and Problems of Inverse type in Control and Signal processing
3 ENIT - Ecole Nationale d'Ingénieurs de Tunis
4 School of Computing [Leeds]

We consider the Cauchy problem of recovering both Neumann and Dirichlet data on the inner part of the boundary of an annular domain, from measurements of a harmonic function on some part of the outer boundary. The ultimate goal is to compute the impedance or Robin coefficient, which is the quotient of these extended data, on the inner boundary. This impedance gives information on the location and extent of a possible corroded area in the internal wall of the domain. Using tools from complex analysis and best approximation in Hardy classes, we present constructive and robust identification schemes validated by a thorough numerical study.

Mots clés: approximation; Inverse problems; Cauchy problems; harmonic functions; analytic functions; Hardy spaces; approximation.

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Mohamed Jaoua, Juliette Leblond, Moncef Mahjoub, Jonathan Partington. Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains. [Research Report] RR-6456, INRIA. 2008. ⟨inria-00258512v2⟩