Hostname: page-component-6bf8c574d5-l72pf Total loading time: 0 Render date: 2025-03-08T02:26:05.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolution of linear magnetostatic inverse problem using iterative regularization*

Published online by Cambridge University Press:  15 November 2000

S. Bégot ,
E. Voisin ,
P. Hiebel ,
J. M. Kauffmann  and
E. Artioukhine
S. Bégot*
Affiliation:
ALSTOM Industries c/o IGE, 2 avenue Jean Moulin, 90000 Belfort, France
E. Voisin
Affiliation:
ALSTOM Industries c/o IGE, 2 avenue Jean Moulin, 90000 Belfort, France
P. Hiebel
Affiliation:
IGE, 2 avenue Jean Moulin, 90000 Belfort, France
J. M. Kauffmann
Affiliation:
IGE, 2 avenue Jean Moulin, 90000 Belfort, France
E. Artioukhine
Affiliation:
IGE, 2 avenue Jean Moulin, 90000 Belfort, France
*
[email protected]
Get access

Abstract

This paper deals with the solution of linear inverse problems in magnetostatics. The case the authors have broached is finding the current density on the basis of magnetic field values. Solving this kind of equation is an ill-posed problem. Exact magnetic field values and measured values lead to different cases, each of which is presented. To solve them, the authors use the conjugate gradient method with iterative regularization. They present numerical results for the design of magnets, gradient and shim coils, and numerical results for the problem of recovering current density values from measured field values.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 12 , Issue 2 , November 2000 , pp. 123 - 131
Copyright
© EDP Sciences, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This paper has been submitted at NUMELEC 2000.

References

A. Tikhonov, V. Arsenin, Solutions of ill-posed problems (Mir, 1977).
Adamiak, K., Int. J. Numer. Methods Eng. 17, 1187 (1981). CrossRef
K. Pawluk, Field Synthesis in Computational Magnetics (Chapman & Hall, London, 1995).
P. Neittaanmäki, Inverse problems and optimal design in electricity and magnetism (Clarendon Press, Oxford, 1996).
Hoult, D.I., Deslauriers, R., J. Magn. Res. A 108, 9 (1994). CrossRef
A. Djerdir, P. Hiebel, E. Voisin, J.M. Kauffmann, Inverse problem in conical magnets without yoke, Proceedings of the International Conference on Electrical Machines, Istanbul, Turkey, 1998, pp. 2155-2160.
Pissanetzky, S., IEEE Trans. Magn. 28, 1961 (1992). CrossRef
Thompson, M.R., Brown, R.W., Srivastava, V.C., IEEE Trans. Magn. 30, 108 (1994). CrossRef
Turner, R., Magn. Reson. Imaging 11, 903 (1993). CrossRef
Russenschuck, S. et al., Eur. Phys. J. AP 1, 93 (1998). CrossRef
Brauer, H., Kosch, O., Tenner, U., Wiechmann, H., Arlt, A., IEEE Trans. Magn. 32, 1318 (1996).
O.M. Alifanov, E.A. Artyukhin, S.V. Rumyantsev, Extreme methods for solving ill-posed problems with applications to inverse heat transfer problems (Begell house, 1995).
J.D. Jackson, Classical electrodynamics, 3rd edn. (Wiley, New York, 1999).
J. Hadamard, Lectures on Cauchy's problem in linear partial differential equation (Yale University Press, New Haven, 1923).
Hansen, P.C., BIT 27, 543 (1987). CrossRef
D.G. Luenberger, Linear and nonlinear programming, 2nd edn. (Addison Wesley, 1989).
A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagola, Numerical Methods for the solution of ill-posed problems (Kluwer Academic Publishers, 1995).
Roméo, F., Hoult, D.I., Magn. Reson. Med. 1, 44 (1984). CrossRef