Numerical Methods for the Landau-Lifshitz-Gilbert Equation

  • L’ubomír Baňas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)


In this paper we give an overview of the numerical methods for the solution of the Landau-Lifshitz-Gilbert equation. We discuss advantages of the presented methods and perform numerical experiments to demonstrate their performance. We also discuss the coupling with Maxwell’s equations.


Projection Method Large Time Step Midpoint Rule Geometric Integration Euler Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Prohl, A.: Computational micromagnetism. In: Advances in numerical mathematics, Teubner, Leipzig, vol. xvi (2001)Google Scholar
  2. 2.
    Wang, X.P., García-Cervera, C.J., Weinan, E.: A Gauss-Seidel projection method for micromagnetics simulations. J. Comput. Phys. 171, 357–372 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Weinan, E., Wang, X.-P.: Numerical methods for the Landau-Lifshitz equation. SIAM J. Numer. Anal. 38, 1647–1665 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Yang, B., Fredkin, D.R.: Dynamical micromagnetics by the finite element method. IEEE Trans. Mag. 34, 3842–3852 (1998)CrossRefGoogle Scholar
  5. 5.
    Suess, D., Tsiantos, V., Schrefl, T., Fidler, J., Scholz, W., Forster, H., Dittrich, R., Miles, J.J.: Time resolved micromagnetics using a preconditioned time integration method. J. Magn. Magn. Mater. 248, 298–311 (2002)CrossRefGoogle Scholar
  6. 6.
    Monk, P., Vacus, O.: Accurate discretization of a nonlinear micromagnetic problem. Comput. Methods Appl. Mech. Eng. 190, 5243–5269 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Lewis, D., Nigam, N.: Geometric integration on spheres and some interesting applications. J. Comput. Appl. Math. 151, 141–170 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Spargo, A.W., Ridley, P.H.W., Roberts, G.W.: Geometric integration of the Gilbert equation. J. Appl. Phys. 93, 6805–6807 (2003)CrossRefGoogle Scholar
  9. 9.
    Joly, P., Vacus, O.: Mathematical and numerical studies of nonlinear ferromagnetic materials. M2AN 33, 593–626 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Serpico, C., Mayergoyz, I.D., Bertotti, G.: Numerical technique for integration of the Landau-Lifshitz equation. J. Appl. Phys. 89, 6991–6993 (2001)CrossRefGoogle Scholar
  11. 11.
    Slodička, M., Baňas, L.: A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert system. In: Appl. Math. Comput. (to appear)Google Scholar
  12. 12.
    Krishnaprasad, P.S., Tan, X.: Cayley transforms in micromagnetics. Physica B 306, 195–199 (2001)CrossRefGoogle Scholar
  13. 13.
    Albuquerque, G., Miltat, J., Thiaville, A.: Self-consistency based control scheme for magnetization dynamics. J. Appl. Phys. 89, 6719–6721 (2001)CrossRefGoogle Scholar
  14. 14.
    Mayergoyz, I.D., Serpico, C., Shimizu, Y.: Coupling between eddy currents and Landau Lifshitz dynamics. J. Appl. Phys. 87, 5529–5531 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • L’ubomír Baňas
    • 1
  1. 1.Department of Mathematical AnalysisGhent UniversityGentBelgium

Personalised recommendations