We propose a new robust, accurate, and fast numerical method for solving the Landau-Lifshitz equation which describes the relaxation process of the magnetization distribution in ferromagnetic material. The proposed numerical method is second-order accurate in both space and time. The approach uses the nonlinear multigrid method for handling the nonlinearities at each time step. We perform numerical experiments to show the efficiency and accuracy of the new algorithm on two- and three-dimensional space. The numerical results show excellent agreements with exact analytical solutions, the second-order accuracy in both space and time, and the energy conservation or dissipation property.
Bibliographical noteFunding Information:
This work was supported by a Korea University Grant. The first author (D. Jeong) and the corresponding author (J.S. Kim) greatly appreciate the reviewers for their constructive comments and suggestions, which improved the quality of this paper.
- Crank-Nicolson scheme
- Finite difference method
- Landau-Lifshitz equation
- Micromagnetics simulations
- Multigrid method
ASJC Scopus subject areas
- General Materials Science
- General Physics and Astronomy