An \(\mathbf H\)-\(\psi \) formulation for the three-dimensional eddy current problem in laminated structures
type: Item
instance of: scholarly article
title: An \(\mathbf H\)-\(\psi \) formulation for the three-dimensional eddy current problem in laminated structures
zbMATH Open document ID: 1270.35258
author: Peijun Li
author: Weiying Zheng
published in: Journal of Differential Equations
publication date: 2013-04-17T00:00:00Z
review text: 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).
reviewed by: Rainer Picard
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35Q61
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 78A55
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 6154868
zbMATH Keywords: silicon steel laminates
zbMATH Keywords: magnetic material relation
zbMATH Keywords: transmission problem
zbMATH Keywords: Helmholtz type decomposition
zbMATH Keywords: layered materials
MaRDI profile type: Publication
full work available at URL: j.jde.2013.01.028
OpenAlex ID: W2132740027
DOI: 10.1016/J.JDE.2013.01.028
description: scientific article; zbMATH DE number 6154868