<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this work, the problem of coil design is studied. It is assumed that the structure of the coil is known (i.e., the positions of simple circular coils are ﬁxed) and the problem is to ﬁnd current distribution to obtain the required magnetic ﬁeld in a given region. The unconstrained version of the problem (arbitrary currents are allowed) can be formulated as a Least-SQuares (LSQ) problem. However, the results obtained by solving the LSQ problem are usually useless from the application point of view. Moreover, for higher dimensions the problem is ill-conditioned. To overcome these difﬁculties, a regularization term is sometimes added to the cost function, in order to make the solution smoother. The regularization technique, however, produces suboptimal solutions. In this work, we propose to solve the problem under study using the constrained Quadratic Programming (QP) method. The methods are compared in terms of the quality of the magnetic ﬁeld obtained, and the power of the designed coil. Several 1D and 2D examples are considered. It is shown that for the same value of the maximum current the QP method provides solutions with a higher quality magnetic ﬁeld than the regularization method.</p></abstract>

In this work, the problem of coil design is studied. It is assumed that the structure of the coil is known (i.e., the positions of simple circular coils are ﬁxed) and the problem is to ﬁnd current distribution to obtain the required magnetic ﬁeld in a given region. The unconstrained version of the problem (arbitrary currents are allowed) can be formulated as a Least-SQuares (LSQ) problem. However, the results obtained by solving the LSQ problem are usually useless from the application point of view. Moreover, for higher dimensions the problem is ill-conditioned. To overcome these difﬁculties, a regularization term is sometimes added to the cost function, in order to make the solution smoother. The regularization technique, however, produces suboptimal solutions. In this work, we propose to solve the problem under study using the constrained Quadratic Programming (QP) method. The methods are compared in terms of the quality of the magnetic ﬁeld obtained, and the power of the designed coil. Several 1D and 2D examples are considered. It is shown that for the same value of the maximum current the QP method provides solutions with a higher quality magnetic ﬁeld than the regularization method.

Tikhonov regularization and constrained quadratic programming for magnetic coil design problems

Department of Electrical Engineering AGH University of Science and Technology, al. Mickiewicza 30, 31-231 Cracow, Poland e-mail:

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this work, the problem of coil design is studied. It is assumed that the structure of the coil is known (i.e., the positions of simple circular coils are...

Tikhonov regularization and constrained quadratic programming for magnetic coil design problems

Published Online: Jun 26, 2014

Page range: 249 - 257

Received: Jan 20, 2013

DOI: https://doi.org/10.2478/amcs-2014-0018

Keywords
coil design problem, constrained quadratic programming, Tikhonov regularization

© 2014 Bartłomiej Garda and Zbigniew Galias

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Tikhonov regularization and constrained quadratic programming for magnetic coil design problems

Published Online: Jun 26, 2014

Page range: 249 - 257

Received: Jan 20, 2013

DOI: https://doi.org/10.2478/amcs-2014-0018

Keywordscoil design problem, constrained quadratic programming, Tikhonov regularization

© 2014 Bartłomiej Garda and Zbigniew Galias

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
coil design problem, constrained quadratic programming, Tikhonov regularization