A finite element based heterogeneous multiscale method for the Landau-Lifshitz equation
Lena Leitenmaier, Murtazo Nazarov · Journal of Computational Physics · 2023
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient , a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε ≪ 1 , which would be too expensive to resolve in a conventional simulation.