2022/06/22 by Jingrun Chen, Jianguo Liu, Chen, Jingrun +3
Computer Science · Engineering · Mathematics · #35B27 #65M15 #82D40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2206.10948
openalex publication_date 2022/06/22 · openalex created_date 2022/06/25 · openalex updated_date 2026/07/28
The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagnets. In this work, we establish the convergence between the homogenized solution and the original solution via a Lax equivalence theorem kind of argument. There are a few technical difficulties, including: 1) it is proven the classic choice of corrector to homogenization cannot provide the convergence result in the H1 norm; 2) a boundary layer is induced due to the natural boundary condition; 3) the presence of stray field give rise to a multiscale potential problem. To keep the convergence rates near the boundary, we introduce the Neumann corrector with a high-order modification. Estimates on singular integral for disturbed functions and boundary layer are deduced, to conduct consistency analysis of stray field. Furthermore, inspired by length conservation of magnetization, we choose proper correctors in specific geometric space. These, together with a uniform W1,6 estimate on original solution, provide the convergence rates in the H1 sense.