Published February 2019
| Version v1
Journal article
Magnetic moment estimation and bounded extremal problems
- Others:
- Analyse fonctionnelle pour la conception et l'analyse de systèmes (FACTAS) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Center for Constructive Approximation [Vanderbilt] ; Vanderbilt University [Nashville]
- Department of Earth, Atmospheric and Planetary Sciences [MIT, Cambridge] (EAPS) ; Massachusetts Institute of Technology (MIT)
- Centre de Mathématiques Appliquées (CMA) ; Mines Paris - PSL (École nationale supérieure des mines de Paris) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
- All authors were supported in part by an Inria grant to the associate team Impinge. L. Baratchart, S. Chevillard, J. Leblond and E. A. Lima alsoacknowledge support from the MIT-France seed fund. The research of D. Hardin and the research of E. A. Lima were supported, in part, by the U.S. National Science Foundation under the grants DMS-1521749 and DMS-1521765, respectively.
Description
We consider the inverse problem in magnetostatics for recovering the moment of a planar magnetization from measurements of the normal component of the magnetic field at a distance from the support. Such issues arise in studies of magnetic material in general and in paleomagnetism in particular. Assuming the magnetization is a measure with L^2-density, we construct linear forms to be applied on the data in order to estimate the moment. These forms are obtained as solutions to certain extremal problems in Sobolev classes of functions, and their computation reduces to solving an elliptic differential-integral equation, for which synthetic numerical experiments are presented.
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/hal-01623991
- URN
- urn:oai:HAL:hal-01623991v2
- Origin repository
- UNICA