发表机构
TU Wien（维也纳工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该文将BDF2型有限元积分器推广至含低阶有效场和电流诱导非保守力矩的LLG方程，采用IMEX时间分裂保持线性求解，证明无条件弱收敛并去除CFL限制，数值实验验证理论。
AI 中文摘要
我们将[M. Aldé, M. Feischl, D. Praetorius; BDF2型积分器用于微磁学中Landau-Lifshitz-Gilbert方程：无条件弱收敛于弱解。(Math. Comp., 2026, doi: https://doi.org/10.1090/mcom/4210)]中提出的BDF2型有限元积分器推广到包含低阶有效场贡献和微磁应用中出现的电流诱导非保守力矩的Landau-Lifshitz-Gilbert (LLG)方程。为了在每一步时间步长中保留线性求解的同时纳入这些额外项，我们采用隐式-显式(IMEX)时间分裂。我们的主要定理证明了全离散逼近无条件弱收敛于LLG方程的弱解。该分析去除了[Aldé M., Feischl M., Praetorius D.; Math. Comp., 2026]中在第一步和最后一步时间步长所需的轻微但人为的CFL型限制。此外，在存在Dzyaloshinskii-Moriya相互作用(DMI)的情况下，收敛同样是无条件的，并且不需要[G. Hrkac, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, A. Segatti, and B. Stiftner. Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. (Adv. Comput. Math., 2019. doi: https://doi.org/10.1007/s10444-019-09667-z)]中施加的CFL型限制。数值实验支持理论发现。
英文摘要
We extend the BDF2-type finite-element integrator proposed in [M. Aldé, M. Feischl, D. Praetorius; BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: unconditional weak convergence to weak solutions. (Math. Comp., 2026, doi:10.1090/mcom/4210)] to the Landau-Lifshitz-Gilbert (LLG) equation with lower-order effective-field contributions and current-induced non-conservative torques arising in micromagnetic applications. To incorporate these additional terms while retaining a linear solve at each time step, we employ an implicit-explicit (IMEX) time splitting. Our main theorem proves unconditional weak convergence of the fully discrete approximations towards weak solutions of the LLG equation. The analysis removes the mild but artificial CFL-type restrictions required at the first and final time steps in [Aldé M., Feischl M., Praetorius D.; Math. Comp., 2026]. Furthermore, in the presence of the Dzyaloshinskii-Moriya interaction (DMI), the convergence is likewise unconditional and does not require the CFL-type restriction imposed in [G. Hrkac, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, A. Segatti, and B. Stiftner. Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. (Adv. Comput. Math., 2019. doi: 10.1007/s10444- 019-09667-z)]. Numerical experiments support the theoretical findings.
Comments50 pages, 19 figures
