Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 369125, 15 pages
Research Article

Adjoint Variable Method for the Study of Combined Active and Passive Magnetic Shielding

Peter Sergeant,1,2 Ivan Cimrák,3 Valdemar Melicher,3 Luc Dupré,1 and Roger Van Keer3

1Department of Electrical Energy, Systems and Automation, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
2Department of Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, Schoonmeersstraat 52, 9000 Gent, Belgium
3NfaM2 Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium

Received 18 October 2007; Accepted 28 January 2008

Academic Editor: Alois Steindl

Copyright © 2008 Peter Sergeant et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For shielding applications that cannot sufficiently be shielded by only a passive shield, it is useful to combine a passive and an active shield. Indeed, the latter does the “finetuning” of the field reduction that is mainly caused by the passive shield. The design requires the optimization of the geometry of the passive shield, the position of all coils of the active shield, and the real and imaginary components of the currents (when working in the frequency domain). As there are many variables, the computational effort for the optimization becomes huge. An optimization using genetic algorithms is compared with a classical gradient optimization and with a design sensitivity approach that uses an adjoint system. Several types of active and/or passive shields with constraints are designed. For each type, the optimization was carried out by all three techniques in order to compare them concerning CPU time and accuracy.