# American Institute of Mathematical Sciences

June  2015, 8(3): 579-605. doi: 10.3934/dcdss.2015.8.579

## 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 fur Angewandte Mathematik und Physik (IAMP), Technikumstrasse 9, Postfach, CH-8401 Winterthur, Switzerland 3 Technische Universität Berlin, Institut für Mathematik, Str. des 17. Juni 136, Sekr. MA 4-5, D-10623 Berlin, Germany

Received  November 2013 Revised  April 2014 Published  October 2014

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.
Citation: Serge Nicaise, Simon Stingelin, Fredi Tröltzsch. Optimal control of magnetic fields in flow measurement. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 579-605. doi: 10.3934/dcdss.2015.8.579
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