Micromagnetics studies magnetic behavior of ferromagnetic materials at sub-micrometer length scales. These scales are large enough to use a continuum PDE model and are small enough to resolve important magnetic structures such as domain walls, vortices and skyrmions. The dynamics of the magnetic distribution in a ferromagnetic material is governed by the Landau- Lifshitz equation. This equation is highly nonlinear and has a non-convex constraint that the magnitude of the magnetization is constant. We present explicit and implicit mimetic finite difference schemes for the Landau-Lifshitz equation, which preserve the magnitude of the magnetization. These schemes work on general polytopal meshes, which provide enormous flexibility to model magnetic devices with various shapes. 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. This is a joint work with Konstantin Lipnikov and Jon Wilkening.