A radial basis function-finite difference method for solving Landau–Lifshitz–Gilbert equation including Dzyaloshinskii-Moriya interaction

This paper investigates a numerical method for solving the two-dimensional Landau–Lifshitz–Gilbert (LLG) equation, governing the dynamics of the magnetization in ferromagnetic materials. Specifically, we incorporate the Dzyaloshinskii–Moriya interaction into the LLG equation—a crucial factor for the creation and stabilization of magnetic skyrmions. We propose a local meshless method that utilizes radial basis function-finite difference (RBF-FD) for spatial discretization and the Crank–Nicolson scheme for temporal discretization, along with an extrapolation technique to handle the nonlinear terms. We demonstrate the method’s accuracy, efficiency, and adaptability through numerical tests on domains of various shapes, showcasing its practical utility in simulating real-world magnetic phenomena and advanced materials.