A Two-dimensional eddy current model using thin inductors

Youcef Amirat (1) , Rachid Touzani (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 $x_3$-direction and the inductors are domains with small diameters of order $O(\epsilon)$. The model is derived by taking the limit $\epsilon\to 0$. A convergence rate of $O(\epsilon^\alpha)$ with $0<\alpha<1/2$ in the $L^2$--norm is shown as well as weak convergence in the $W^{1,p}$ spaces for $1< p <2$.

Mots clés: Asymptotic analysis; thin domain; Eddy current problem

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Rachid Touzani. A Two-dimensional eddy current model using thin inductors. Asymptotic Analysis, 2008, 58 (3), pp.171-188. ⟨hal-00085042⟩