An optimum design problem in magnetostatics

Antoine Henrot; Grégory Villemin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 2, page 223-239
  • ISSN: 0764-583X

Abstract

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

How to cite

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Henrot, Antoine, and Villemin, Grégory. "An optimum design problem in magnetostatics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 223-239. <http://eudml.org/doc/245598>.

@article{Henrot2002,
abstract = {In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.},
author = {Henrot, Antoine, Villemin, Grégory},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {shape optimization; optimum design; magnet; numerical examples},
language = {eng},
number = {2},
pages = {223-239},
publisher = {EDP-Sciences},
title = {An optimum design problem in magnetostatics},
url = {http://eudml.org/doc/245598},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Henrot, Antoine
AU - Villemin, Grégory
TI - An optimum design problem in magnetostatics
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 2
SP - 223
EP - 239
AB - In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
LA - eng
KW - shape optimization; optimum design; magnet; numerical examples
UR - http://eudml.org/doc/245598
ER -

References

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  10. [10] M. Pierre and J.R. Roche, Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numer. Math. 65 (1993) 203–217. Zbl0792.65096
  11. [11] O. Pironneau, Optimal shape design for elliptic systems. Springer Series in Computational Physics. Springer, New York (1984). Zbl0534.49001MR725856
  12. [12] J. Simon, Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim. 2 (1980) 649–687. Zbl0471.35077
  13. [13] J. Simon, Variations with respect to domain for Neumann condition. Proceedings of the 1986 IFAC Congress at Pasadena “Control of Distributed Parameter Systems”. 
  14. [14] J. Sokolowski and J.P. Zolesio, Introduction to shape optimization: shape sensitity analysis. Springer Series in Computational Mathematics, Vol. 10, Springer, Berlin (1992). Zbl0761.73003MR1215733

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