Optimal control of magnetic fields  in flow measurement

Serge Nicaise; Simon Stingelin; Fredi Tröltzsch

doi:10.3934/dcdss.2015.8.579

Article Contents

2015, Volume 8, Issue 3: 579-605. Doi: 10.3934/dcdss.2015.8.579

This issue Previous Article The factorization method for scatterers with different physical properties Next Article On Maxwell's and Poincaré's constants

Optimal control of magnetic fields in flow measurement

1.
Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, F-59313 - Valenciennes Cedex 9
2.
ZHAW School of Engineering, Institut fur Angewandte Mathematik und Physik (IAMP), Technikumstrasse 9, Postfach, CH-8401 Winterthur
3.
Technische Universität Berlin, Institut für Mathematik, Str. des 17. Juni 136, Sekr. MA 4-5, D-10623 Berlin

Received: November 2013

Revised: April 2014

Published: July 2015

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Abstract

Optimal control problems are considered for transient magnetization processes arising from electromagnetic flow measurement. The magnetic fields are generated by an induction coil and are defined in 3D spatial domains that include electrically conducting and nonconducting regions. Taking the electrical voltage in the coil as control, the state equation for the magnetic field and the electrical current generated in the induction coil is a system of integro-differential evolution Maxwell equations. The aim of the control is a fast transition of the magnetic field in the conduction region from an initial polarization to the opposite one. First-order necessary optimality condition and numerical methods of projected gradient type are discussed for associated optimal control problems. To deal with the extremely long computing times for this problem, model reduction by standard proper orthogonal decomposition is applied. Numerical tests are shown for a simplified geometry and for a 3D industrial application.

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Mathematics Subject Classification: Primary: 49K20, 35K565; Secondary: 49M05, 78A25.

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