On two optimal control problems for magnetic fields

Nicaise, Serge; Stingelin, Simon; Tröltzsch, Fredi

doi:10.21256/zhaw-4781

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-4781

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	On two optimal control problems for magnetic fields
Authors:	Nicaise, Serge Stingelin, Simon Tröltzsch, Fredi
DOI:	10.21256/zhaw-4781 10.1515/cmam-2014-0022
Published in:	Computational Methods in Applied Mathematics
Volume(Issue):	14
Issue:	4
Page(s):	555
Pages to:	573
Issue Date:	2014
Publisher / Ed. Institution:	De Gruyter
ISSN:	1609-4840 1609-9389
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):	510: Mathematics
Abstract:	Two optimal control problems for instationary magnetization processes are considered in 3D spatial domains that include electrically conducting and non-conducting 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 non-conducting 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 (http://www.nationallizenzen.ch)
URI:	https://digitalcollection.zhaw.ch/handle/11475/15840
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Applied Mathematics and Physics (IAMP)
Appears in collections:	Publikationen School of Engineering

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Nicaise, S., Stingelin, S., & Tröltzsch, F. (2014). On two optimal control problems for magnetic fields. Computational Methods in Applied Mathematics, 14(4), 555–573. https://doi.org/10.21256/zhaw-4781

Nicaise, S., Stingelin, S. and Tröltzsch, F. (2014) ‘On two optimal control problems for magnetic fields’, Computational Methods in Applied Mathematics, 14(4), pp. 555–573. Available at: https://doi.org/10.21256/zhaw-4781.

S. Nicaise, S. Stingelin, and F. Tröltzsch, “On two optimal control problems for magnetic fields,” Computational Methods in Applied Mathematics, vol. 14, no. 4, pp. 555–573, 2014, doi: 10.21256/zhaw-4781.

NICAISE, Serge, Simon STINGELIN und Fredi TRÖLTZSCH, 2014. On two optimal control problems for magnetic fields. Computational Methods in Applied Mathematics. 2014. Bd. 14, Nr. 4, S. 555–573. DOI 10.21256/zhaw-4781

Nicaise, Serge, Simon Stingelin, and Fredi Tröltzsch. 2014. “On Two Optimal Control Problems for Magnetic Fields.” Computational Methods in Applied Mathematics 14 (4): 555–73. https://doi.org/10.21256/zhaw-4781.

Nicaise, Serge, et al. “On Two Optimal Control Problems for Magnetic Fields.” Computational Methods in Applied Mathematics, vol. 14, no. 4, 2014, pp. 555–73, https://doi.org/10.21256/zhaw-4781.