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A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation
Computer Modeling in Engineering & Sciences 2005, 9(2), 151-178. https://doi.org/10.3970/cmes.2005.009.151
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In this paper we are concerned with the integration of a semi-discretized version of the Landau-Lifshitz equation, which is fundamental to describe the magnetization dynamics in micro/nano-scale magnetic systems. The resulting ordinary differential equations at the interior grid points are numerically integrated by a combination of the group preserving scheme derived by Liu (2004a) and the fourth-order Runge-Kutta method, abbreviated as GPS-RK4. The new method not only conserves the magnetization magnitude and has the fourth-order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation, namely the free energy is decreasing with time. In the limit of zero damping, the GPS-RK4 also well conserves the free energy constant in time. Numerical tests are performed to confirm the effectiveness of GPS-RK4.Keywords
Computational micromagnetics, group preserving scheme, Runge-Kutta method, Landau-Lifshitz equation.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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