A two-dimensional eddy current model using thin inductors

Article type: Research Article

Authors: Amirat, Youcef | Touzani, Rachid

Affiliations: Laboratoire de Mathématiques, UMR CNRS 6620, Université Blaise Pascal (Clermont–Ferrand), 63177 Aubière cedex, France. E-mail: {Youcef.Amirat, Rachid.Touzani}@math.univ-bpclermont.fr

Abstract: We derive a mathematical model for eddy currents in two-dimensional geometries where the conductors are thin domains. We assume that the current flows in the x3-direction and the inductors are domains with small diameters of order O(ε). The model is derived by taking the limit ε→0. A convergence rate of O(εα) with 0<α<1/2 in the L2-norm is shown as well as weak convergence in the W1,p spaces for 1<p<2.

Journal: Asymptotic Analysis, vol. 58, no. 3, pp. 171-188, 2008