Volume 44, pp. 250-270, 2015.

A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations

Lubomir Baňas, Marcus Page, and Dirk Praetorius

Abstract

We consider the lowest-order finite 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 time step. One of the algorithms is decoupled in the sense that it consists of the sequential computation of the magnetization and afterwards the magnetic and electric field. Under some mild assumptions on the effective field, 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.

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Key words

Maxwell-LLG, linear scheme, ferromagnetism, convergence

AMS subject classifications

65N30, 65N50

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