2021/11/22 by Lena Leitenmaier, Murtazo Nazarov, Leitenmaier, Lena +1
Computer Science · Engineering · Mathematics · #65M12 #65M60 #78M10 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2111.11197
openalex publication_date 2021/11/22 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28
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.