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
2 CMA - Centre de Mathématiques Appliquées

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.

Mots clés: Inverse source problems; Meromorphic approximation; Potential theory

Domaines: Automatique

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, 2006, 25, pp.41-53. ⟨hal-00504716⟩