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
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 
@article{ETNA_2015__44__a18,
     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},
     year = {2015},
     volume = {44},
     zbl = {1327.65233},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a18/}
}
TY  - JOUR
AU  - Baňas,  Lubomir
AU  - Page,  Marcus
AU  - Praetorius,  Dirk
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JO  - Electronic transactions on numerical analysis
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EP  - 270
VL  - 44
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%A Page,  Marcus
%A Praetorius,  Dirk
%T A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equations
%J Electronic transactions on numerical analysis
%D 2015
%P 250-270
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%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a18/
%G en
%F ETNA_2015__44__a18
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/