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Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices

Laurent Baratchart 1 Juliette Leblond 1 Jean-Paul Marmorat 2
1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 CMA - Centre de Mathématiques Appliquées
Abstract : We show that the inverse monopolar or dipolar source problem in a 3D ball from overdetermined Dirichlet-Neumann data on the boundary sphere reduces to a family of 2D inverse branchpoint problems in cross sections of the sphere, at least when there are finitely many sources. We adapt from [7] an approach to these 2D inverse problem which is based on meromorphic approximation, and we present numerical results.
Keywords : Inverse source problems Meromorphic approximation Potential theory
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Submitted on : Wednesday, July 21, 2010 - 11:23:35 AM
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Laurent Baratchart, Juliette Leblond, Jean-Paul Marmorat. Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices. Electronic Transactions on Numerical Analysis, Kent State University Library, 2006, 25, pp.41-53. ⟨hal-00504716⟩

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