An optimum design problem in magnetostatics
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 2, p. 223-239

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.

DOI : https://doi.org/10.1051/m2an:2002012
Classification:  49J20,  49Q10,  65K10,  78A30
Keywords: shape optimization, optimum design, magnet, numerical examples
@article{M2AN_2002__36_2_223_0,
     author = {Henrot, Antoine and Villemin, Gr\'egory},
     title = {An optimum design problem in magnetostatics},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {2},
     year = {2002},
     pages = {223-239},
     doi = {10.1051/m2an:2002012},
     zbl = {1054.49030},
     mrnumber = {1906816},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_2_223_0}
}
Henrot, Antoine; Villemin, Grégory. An optimum design problem in magnetostatics. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 2, pp. 223-239. doi : 10.1051/m2an:2002012. http://www.numdam.org/item/M2AN_2002__36_2_223_0/

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