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IMA Journal of Applied Mathematics Advance Access published online on December 18, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn041
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Mohamed Jaoua

Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, F-06108 Nice, France

Juliette Leblond

Institut National de Recherche en Informatique et Automatique, BP 93, 06902 Sophia Antipolis, France

Moncef Mahjoub{dagger}

Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de I'Ingénieur-Ecole Nationale d'Ingnieurs de Tunis, BP 37, 1002 Tunis Belvedere, Tunisia

Jonathan R. Partington

School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

{dagger} Email: moncef.mahjoub{at}lamsin.rnu.tn

Received on March 20, 2008; Revision received September 27, 2008. Accepted on November 7, 2008

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. Using tools from complex analysis and best approximation in Hardy classes, we present a family of fast data completion algorithms which are shown to provide constructive and robust identification schemes. These are applied to the computation of an impedance or Robin coefficient and are validated by a thorough numerical study.

Keywords: inverse problems; Cauchy problems; harmonic functions; analytic functions; Hardy spaces; approximation.


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