Analysis of an eddy current and micromagnetic model

Abstract

We consider a coupled eddy current and micromagnetic model describing the behaviour of dynamic electromagnetic phenomena in applications such as disk write heads. We first prove the existence of a weak solution to this nonlinear problem. Then we outline a numerical time-stepping scheme. Since the numerical method requires a nonstandard mixed boundary value eddy current problem to be solved at each time step, we show the existence and uniqueness of a solution for the corresponding eddy current problem. This is accomplished using an image principle and the verification of a suitable Babuška–Brezzi condition.

Keywords:

• Eddy current
• Micromagnetic model
• Landau–Lifshitz equation
• Babuška-Brezzi condition

Keywords:

• 2000 Mathematics Subject Classifications: 35Q60

Acknowledgement

J. Sun was supported by a DoD grant DAAD19-03-1-0375.