Numerical study of nonlinear ferromagnetic materials
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.
scientific article; zbMATH DE number 1956721
scientific article