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Title: On two optimal control problems for magnetic fields
Authors : Nicaise, Serge
Stingelin, Simon
Tröltzsch, Fredi
Published in : Computational Methods in Applied Mathematics
Volume(Issue) : 14
Issue : 4
Pages : 555
Pages to: 573
Publisher / Ed. Institution : De Gruyter
Issue Date: 2014
License (according to publishing contract) : Licence according to publishing contract
Type of review: Peer review (publication)
Language : English
Subjects : Evolution Maxwell Equations; Proper orthogonal decomposition; Numerical solution; Adjoint equation; Model reduction; Optimal control; Degenerate parabolic equation; Vector potential formulation; Induction law
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: Two optimal control problems for instationary magnetization processes are considered in 3D spatial domains that include electrically conducting and nonconducting regions. The magnetic fields are generated by induction coils. In the first model, the induction coil is considered as part of the conducting region and the electrical current is taken as control. In the second, the coil is viewed as part of the nonconducting region and the electrical voltage is the control. Here, an integro-differential equation accounts for the magnetic induction law that couples the given electrical voltage with the induced electrical current in the induction coil. We derive first-order necessary optimality conditions for the optimal controls of both problems. Based on them, numerical methods of gradient type are applied. Moreover, we report on the application of model reduction by POD that lead to tremendous savings. Numerical tests are presented for academic 3D geometries but also for a real-world application.
Further description : Erworben im Rahmen der Schweizer Nationallizenzen (
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Publication type: Article in scientific journal
DOI : 10.21256/zhaw-4781
ISSN: 1609-4840
Appears in Collections:Publikationen School of Engineering

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