Geodesic
A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 250-270.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 65N30, 65N50
Keywords: Maxwell-LLG, linear scheme, ferromagnetism, convergence 
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     author = {Ba\v{n}as, Lubomir and Page, Marcus and Praetorius, Dirk},
     title = {A convergent linear finite element scheme for the {Maxwell-Landau-Lifshitz-Gilbert} equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {250--270},
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     volume = {44},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a18/}
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Baňas, Lubomir; Page, Marcus; Praetorius, Dirk. A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 250-270. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a18/