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L. Banas, M. Page, D. Praetorius:
"A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations";
Electron. Trans. Numer. Anal., 44 (2015), S. 250 - 270.

Abstract. We consider a lowest-order nite element discretization of the nonlinear system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two algorithms are proposed to numerically solve this problem, both of which only require the solution of at most two
linear systems per timestep. One of the algorithms is fully decoupled in the sense that each timestep consists of the sequential computation of the magnetization and afterwards the magnetic and electric eld. Under some mild assumptions on the e ective eld, we show
that both algorithms converge towards weak solutions of the MLLG system. Numerical experiments for a micromagnetic benchmark problem demonstrate the performance of the proposed algorithms.

Maxwell-LLG, linear scheme, ferromagnetism, convergence.

http://etna.ricam.oeaw.ac.at/vol.44.2015/pp250-270.dir/pp250-270.pdf