On a decoupled linear FEM integrator for eddy-current-LLG

Abstract

We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau–Lifshitz–Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover exchange, anisotropy, applied field and magnetic field (stemming from the eddy-current equation). Even though the considered problem is nonlinear, our scheme requires only the solution of two linear systems per time-step. Moreover, our algorithm decouples both equations so that in each time-step, one linear system is solved for the magnetization, and afterwards one linear system is solved for the magnetic field. Unconditional convergence – at least of a subsequence – towards a weak solution is proved, and our analysis even provides existence of such weak solutions. Numerical experiments with micromagnetic benchmark problems underline the performance and the stability of the proposed algorithm.

Keywords:

• quasi-static Maxwell-LLG
• eddy-current equation
• finite element
• ferromagnetism
• convergence analysis

AMS Subject Classifications:

• 65M12
• 65N30
• 35K55

Acknowledgements

The authors acknowledge financial support through the Austrian Science Fund (FWF) project P21732, the Vienna Science and Technology Fund (WWTF) project MA09-29, and the Australian Research Council (ARC) project DP120101886.