Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T06:44:15.977Z Has data issue: false hasContentIssue false
  • English
  • Français

An Optimum Design Problem in Magnetostatics

Published online by Cambridge University Press:  15 May 2002

Antoine Henrot  and
Grégory Villemin
Antoine Henrot
Affiliation:
École des Mines de Nancy and Institut Elie Cartan, BP 239 54506 Vandœuvre-lès-Nancy, France. [email protected].
Grégory Villemin
Affiliation:
Centre de Recherche Valeo - Systèmes d'essuyage, Z.A. de l'Agiot, 78231 La Verrière, France. [email protected].
Get access

Abstract

In this paper, we are interested in finding the optimal shapeof a magnet. The criterion to maximize is the jump of theelectromagnetic field between two different configurations.We prove existence of an optimal shape into a natural classof domains. We introduce a quasi-Newton type algorithm whichmoves the boundary. This method is very efficient to improvean initial shape. We give some numerical results.

Keywords

Shape optimizationoptimum designmagnetnumerical examples.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 223 - 239
Copyright
© EDP Sciences, SMAI, 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.)

References

S. Agmon, Lectures on Elliptic Boundary Value Problems. Van Nostrand Math Studies (1965).
J. Baranger, Analyse Numérique. Hermann, Paris (1991).
Chenais, D., On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (1975) 189-289. CrossRef
D. Chenais, Sur une famille de variétés à bord lipschitziennes, application à un problème d'identification de domaine. Ann. Inst. Fourier (Grenoble) 4 (1977) 201-231.
R. Dautray and J.L. Lions (Eds.), Analyse mathématique et calcul numérique, Vol. I and II. Masson, Paris (1984).
J.E. Dennis and R.B. Schnabel, Numerical Methods for unconstrained optimization. Prentice Hall (1983).
E. Durand, Magnétostatique. Masson, Paris (1968).
A. Henrot and M. Pierre, Optimisation de forme (to appear).
Pierre, M. and Roche, J.R., Computation of free sufaces in the electromagnetic shaping of liquid metals by optimization algorithms. Eur. J. Mech. B Fluids 10 (1991) 489-500.
Pierre, M. and Roche, J.R., Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numer. Math. 65 (1993) 203-217. CrossRef
O. Pironneau, Optimal shape design for elliptic systems. Springer Series in Computational Physics. Springer, New York (1984).
Simon, J., Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim. 2 (1980) 649-687. CrossRef
J. Simon, Variations with respect to domain for Neumann condition. Proceedings of the 1986 IFAC Congress at Pasadena ``Control of Distributed Parameter Systems".
J. Sokolowski and J.P. Zolesio, Introduction to shape optimization: shape sensitity analysis. Springer Series in Computational Mathematics, Vol. 10, Springer, Berlin (1992). CrossRef