On two optimal control problems for magnetic fields
Please always quote using this URN:urn:nbn:de:0296-matheon-12898
- 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 condition 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.
Author: | Serge Nicaise, Stingelin Simon, Tröltzsch Fredi |
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URN: | urn:nbn:de:0296-matheon-12898 |
Referee: | Dietmar Hömberg |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2014/05/19 |
Release Date: | 2014/05/19 |
Tag: | Evolution Maxwell equations; model reduction; necessary optimality conditions; optimal control; vector potential formulation |
Institute: | Technische Universität Berlin |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations |
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M05 Methods based on necessary conditions | |
Preprint Number: | 1061 |