Numerical study of nonlinear ferromagnetic materials
type: Item
instance of: scholarly article
title: Numerical study of nonlinear ferromagnetic materials
zbMATH Open document ID: 1027.78002
DOI: 10.1016/S0168-9274(03)00010-2
author: M. Slodička
author: Ivan Cimrák
published in: Applied Numerical Mathematics
publication date: 2003-07-30T00:00:00Z
review text: The authors consider quasi-state Maxwell equations of the form \[ \nabla\times H=\sigma E+J_0,\;\partial_t B+\nabla\times E=0,\tag{1} \] where \(J_0\) is the current density, \(\sigma>0\) denotes the conductivity of a medium, \(B\) -- the magnetic induction, \(H\) -- the magnetic field, \(M\) -- the magnetization, \(E\) -- the electric field with \(B=\mu_0 (H+M)\); \(\mu_0\) denotes the magnetic permeability of free space. The main goal of this paper is to present two new approximation schemes for the time discretization of a quasi-static Maxwell-LLG system \[ \mu_0\partial_t H+\sigma^{-1}\nabla\times \nabla \times H=\sigma^{-1} \nabla\times J_0-\mu_0 \partial_tM,\;\partial_t M=f(H,M) \tag{2} \] which is obtained from (1) eliminating \(B\) and \(E\). The authors design a linear and a nonlinear numerical algorithm for the computation of the vector field \(M\). For the time discretization for \(H\) they use Rothe's method. Assuming that the exact solution of (2) is bounded, the authors derive the error estimates for the proposed numerical schemes.
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78M25
zbMATH DE Number: 1956721
zbMATH Keywords: Ferromagnetism
zbMATH Keywords: Maxwell-Landau-Lifshitz-Gilbert system
zbMATH Keywords: Quasi-static electromagnetic field
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: s0168-9274(03)00010-2
OpenAlex ID: W2052934218
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description: scientific article; zbMATH DE number 1956721