https://hal-uphf.archives-ouvertes.fr/hal-03142630Nicaise, SergeSergeNicaiseLAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015 - UVHC - Université de Valenciennes et du Hainaut-Cambrésis - CNRS - Centre National de la Recherche Scientifique - INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-FranceStingelin, SimonSimonStingelinZHAW School of Engineering - ZHAW - Zürich University of Applied SciencesTröltzsch, FrediFrediTröltzschTU - Technische Universität BerlinOptimal control of magnetic fields in flow measurementHAL CCSD2015numerical solutionoptimal controlinduction lawEvolution Maxwell equationsvector potential formulationadjoint equationproper orthogonal decomposition.model reductiondegenerate parabolic equationintegro-differential equation.[MATH] Mathematics [math]Cagniard, Julie2021-02-16 10:55:202021-10-19 18:38:162021-02-16 10:55:20enJournal articles10.3934/dcdss.2015.8.5791Optimal 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.