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

Kim-Ngan Le, Marcus Page, Dirk Praetorius, Thanh Tran

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10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1051-1067
Number of pages17
JournalApplicable Analysis
Issue number5
Publication statusPublished - 1 Jan 2015
Externally publishedYes


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

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