2021/04/07 by Lena Leitenmaier, Leitenmaier, Lena, Olof Runborg +1 · 1 citation
Computer Science · Engineering · Mathematics · #35B27 #65M15 #78M40 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2104.03206
openalex publication_date 2021/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider several possible ways to set up Heterogeneous\nMultiscale Methods for the Landau-Lifshitz equation with a highly oscillatory\ndiffusion coefficient, which can be seen as a means to modeling rapidly varying\nferromagnetic materials. We then prove estimates for the errors introduced when\napproximating the relevant quantity in each of the models given a periodic\nproblem, using averaging in time and space of the solution to a corresponding\nmicro problem. In our setup, the Landau-Lifshitz equation with highly\noscillatory coefficient is chosen as the micro problem for all models. We then\nshow that the averaging errors only depend on \ε, the size of the\nmicroscopic oscillations, as well as the size of the averaging domain in time\nand space and the choice of averaging kernels.\n