Hostname: page-component-7dd5485656-7jgsp Total loading time: 0 Render date: 2025-10-30T22:10:02.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolution of a linear and a nonlinear inverse problemin magnetostatics

Published online by Cambridge University Press:  24 July 2002

S. Bégot ,
E. Artioukhine ,
P. Hiebel  and
J. M. Kauffmann
S. Bégot*
Affiliation:
L2ES LRE T 31, IGE, 2 avenue Jean Moulin, 90000 Belfort, France
E. Artioukhine
Affiliation:
CREST UMR 6000, IGE, 2 avenue Jean Moulin, 90000 Belfort, France
P. Hiebel
Affiliation:
L2ES LRE T 31, IGE, 2 avenue Jean Moulin, 90000 Belfort, France
J. M. Kauffmann
Affiliation:
L2ES LRE T 31, IGE, 2 avenue Jean Moulin, 90000 Belfort, France
*
sylvie.begot@univ-fcomte.fr
Get access

Abstract

This paper deals with the solution of inverse problems in magnetostatics. The cases the authors have broached are finding the current density or positions of air coils on the basis of magnetic field measurements. These problems are ill-posed, so regularization techniques are needed. The authors discuss the main iterative regularization principles, and the stability issues of these inverse problems. This method is applied to MRI magnets. Numerical results are presented.

Keywords

Information

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 19 , Issue 2 , August 2002 , pp. 141 - 150
Copyright
© EDP Sciences, 2002

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.)

Article purchase

Temporarily unavailable

References

V.G. Romanov, S.I. Kabanikhin, Inverse problems for Maxwell's Equations (VSP, 1994)
Russenschuck, S. et al., Eur. Phys. J. AP 1, 93 (1998) CrossRef
Bettini, P., Bellina, F., Formisano, A., Martone, R., Stella, A., Trevisan, F., Eur. Phys. J. AP 13, 51 (2001) CrossRef
J.T. Nenonen, IEEE Eng. Med. Biol. 487 (1994)
Bégot, S., Voisin, E., Hiebel, P., Kauffmann, J.M., Artioukhine, E., Eur. Phys. J. AP 12, 123 (2000) CrossRef
J.D. Jackson, Classical electrodynamics, 3rd edn. (Wiley: New York, 1999)
A.N. Tikhonov, V. Arsenin, Methods for solving ill-posed problems (Mir, 1974)
A.N. Tikhonov, A.S. Leonov, A.G. Yagola, Nonlinear ill-posed problems (Chapman & Hall: London, 1998)
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)
S.F. Gilyazov, N.L. Gol'dman, Regularization of ill-posed problems by iteration methods (Kluwer academic publishers, 2000)
P.E. Gill, W. Murray, M.H. Wright, Practical optimization (Academic Press, New York, 1981)
R.F. Curtain, A.J. Pritchard, Functional analysis in modern applied mathematics (Academic Press, New York, 1977)
S. Bégot, E. Voisin, P. Hiebel, J.M. Kauffmann, E. Artioukhine, IEEE Trans. Magn., accepted for publication
R. Kress, Linear integral equations (Springer-Verlag, Berlin, 1989)