TY - GEN A1 - Nicaise, Serge A1 - Simon, Stingelin A1 - Fredi, Tröltzsch T1 - On two optimal control problems for magnetic fields N2 - 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. KW - Evolution Maxwell equations KW - vector potential formulation KW - optimal control KW - necessary optimality conditions KW - model reduction Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1289 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12898 ER -