An iterative approximation scheme for the Landau-Lifshitz-Gilbert equation

Journal of Computational and Applied Mathematics

Volumn 169, Issue 1, 2004, Pages 17-32

  Cimrák, Ivan ^a   Slodička, Marián ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Ferromagnets; Landau Lifshitz Gilbert equation; Micromagnetism

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONTROL NONLINEARITIES; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES;

FIXED POINT TECHNIQUE; LANDAU-LIFSHITZ-GILBERT EQUATION;

COMPUTATION THEORY;

MAGNETISM; MATHEMATICAL METHOD;

EID: 3042554534     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.10.022     Document Type: Article

References (24)

1. Anzellotti G. Baldo S. Visintin A. Asymptotic behavior of the Landau-Lifshitz model of ferromagnetism Appl. Math. Optim. 23 3 1991 171-192
2. Bertotti G. Serpico C. Mayergoyz I.D. Nonlinear magnetization dynamics under circularly polarized field Phys. Rev. Lett. 86 4 2001 724-727
3. Chen Y. Dirichlet boundary value problems of Landau-Lifshitz equation Comm. Partial Differential Equations 25 1-2 2000 101-124
4. Chen Y. Existence and singularities for the Dirichlet boundary value problems of Landau-Lifshitz equations Nonlinear Anal. Theory Methods Appl. 48A 3 2002 411-426
5. W. E, X.-P. Wang, Numerical methods for the Landau-Lifshitz equation, SIAM J. Numer. Anal. 38(5) (2000)
6. Guo B. Ding S. Neumann problem for the Landau-Lifshitz-Maxwell system in two dimensions Chinese Ann. Math. Ser. B 22 4 2001 529-540
7. Guo B. Su F. Global weak solution for the Landau-Lifshitz-Maxwell equation in three space dimensions J. Math. Anal. Appl. 211 1 1997 326-346
8. Haddar H. Joly P. Effective boundary conditions for thin ferromagnetic layers: the one-dimensional model SIAM J. Appl. Math. 61 4 2001 1386-1417
9. Joly J.L. Métivier G. Rauch J. Electromagnetic wave propagation in presence of a ferromagnetic material ESAIM Proc. 3 1998 85-99
10. Joly J.L. Métivier G. Rauch J. Global solutions to Maxwell equations in a ferromagnetic medium Ann. Henri Poincaré 1 2 2000 307-340
11. Joly P. Komech A. Vacus O. On transitions to stationary states in a Maxwell-Landau-Lifschitz-Gilbert system SIAM J. Math. Anal. 31 2 2000 346-374
12. P. Joly, O. Vacus, Maxwell's equations in a ID ferromagnetic medium: existence and uniqueness of strong solutions, INRIA, Technical Report No. 3052, 1996.
13. Joly P. Vacus O. Mathematical and numerical studies of nonlinear ferromagnetic materials Math. Model. Numer. Anal. 33 3 1999 593-626
14. Landau L.D. Lifshitz E.M. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies Phys. Z. Sowjetunion 8 1935 153-169
15. L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Vol. X, Transl. from the Russian by J.B. Sykes and J.S. Bell, Pergamon Press, Oxford, London, New York, Paris, 1960, 417p.
16. Monk P.B. Vacus O. Error estimates for a numerical scheme for ferromagnetic problems SIAM J. Numer. Anal. 36 3 1998 696-718
17. Monk P.B. Vacus O. Accurate discretization of a nonlinear micromagnetic problem Comput. Methods Appl. Mech. Eng. 190 40-41 2001 5243-5269
18. Prohl A. Computational micromagnetism Advances in Numerical Mathematics Vol. xvi 2001 Teubner Leipzig
19. M. Slodička, L'. Baňas, A numerical scheme for a Maxwell-Landau-Lifschitz-Gilbert system, Appl. Math. Comput., in press.
20. Slodička M. Cimrák I. Numerical study of nonlinear ferromagnetic materials Appl. Numer. Math. 46 1 2003 95-111
21. Su F. Guo B. The global smooth solution for Landau-Lifshitz-Maxwell equation without dissipation J. Partial Differential Equations 11 3 1998 193-208
22. Visintin A. On Landau-Lifshitz' equations for ferromagnetism Japan J. Appl. Math. 2 1985 69-84
23. Weiss P. L'hypothèse du champ moléculaire et la proprièté ferromagnetique J. Physique 6 1907 661-690
24. Zhai J. Existence and behavior of solutions to the Landau-Lifshitz equation SIAM J. Math. Anal. 30 4 1999 833-847