An \(\mathbf H\)-\(\psi \) formulation for the three-dimensional eddy current problem in laminated structures. (English) Zbl 1270.35258
Dropping the displacement current in Maxwell’s equations with conductivity term yields the so-called eddy current problem. The resulting parabolic system has better regularity properties, which can for example be utilized for dealing with nonlinearities. The nonlinearities enter the discussion in this paper via the Nimitzky type magnetic material relation \(B=B(H)\). The transmission problem of a conducting region \(\Omega_{c}\) embedded in a non-conducting complement \(\Omega_{nc}\) with known current density \(J_{s}\) in \(\mathbb{R}^{3}\) is considered. The weak problem is solved by approximation using the horizontal line method (Rothe’s method) and showing convergence to the weak solution. The approach uses a Helmholtz type decomposition of the magnetic field \(H\) involving a potential called \(\psi\) (referred to as \(H\)-\(\psi\) formulation of the eddy current problem in the title). Particular attention is given to the case of layered materials. Specifically silicon steel laminates are considered (ignoring the silicon insulation layers).
Reviewer: Rainer Picard (Dresden)
MSC:
35K55 | Nonlinear parabolic equations |
35Q60 | PDEs in connection with optics and electromagnetic theory |
35Q61 | Maxwell equations |
35K45 | Initial value problems for second-order parabolic systems |
78A55 | Technical applications of optics and electromagnetic theory |
78A25 | Electromagnetic theory (general) |