On Two Optimal Control Problems for Magnetic Fields
-
Serge Nicaise
,
Simon Stingelin
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.
Funding source: Endress+Hauser Flowtec AG Reinach (Switzerland)
© 2014 by De Gruyter
Articles in the same Issue
- Frontmatter
- Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
- Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System
- An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators
- Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media
- Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
- Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters
- Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets
- On Two Optimal Control Problems for Magnetic Fields
Articles in the same Issue
- Frontmatter
- Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
- Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System
- An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators
- Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media
- Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
- Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters
- Superfast Wavelet Transform Using Quantics-TT Approximation. I. Application to Haar Wavelets
- On Two Optimal Control Problems for Magnetic Fields
