An Optimum Design Problem in Magnetostatics

Antoine Henrot; Grégory Villemin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 36.2 (2010): 223-239. <http://eudml.org/doc/194102>.

@article{Henrot2010,
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},
keywords = {Shape optimization; optimum design; magnet; numerical examples.; shape optimization; numerical examples},
language = {eng},
month = {3},
number = {2},
pages = {223-239},
publisher = {EDP Sciences},
title = {An Optimum Design Problem in Magnetostatics},
url = {http://eudml.org/doc/194102},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Henrot, Antoine
AU - Villemin, Grégory
TI - An Optimum Design Problem in Magnetostatics
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
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.; shape optimization; numerical examples
UR - http://eudml.org/doc/194102
ER -

References

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  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. O. Pironneau, Optimal shape design for elliptic systems. Springer Series in Computational Physics. Springer, New York (1984).  
  12. J. Simon, Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim.2 (1980) 649-687.  Zbl0471.35077
  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. J. Sokolowski and J.P. Zolesio, Introduction to shape optimization: shape sensitity analysis. Springer Series in Computational Mathematics, Vol. 10, Springer, Berlin (1992).  Zbl0761.73003

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