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Center for Nonlinear Studies |
The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which pose interesting challenges in developing numerical methods. We present explicit and implicit mimetic finite difference schemes for the Landau-Lifshitz equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection to the unit sphere is used to preserve the magnitude of the magnetization. We will present rigorous convergence tests for the schemes on general meshes that includes distorted and randomized meshes. We will also present numerical simulations for the NIST standard problem #4 and the formation of the domain wall structures in a thin film.