An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation
Year: 2024
Author: Zheyue Fang, Xiaoping Wang
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 3 : pp. 601–635
Abstract
We present a moving mesh finite element method to study the finite-time blowup solution of the Landau-Lifshitz-Gilbert (LLG) equation, considering both the heat flow of harmonic map and the full LLG equation. Our approach combines projection methods for solving the LLG equation with an iterative grid redistribution method to generate adaptive meshes. Through iterative remeshing, we successfully simulate blowup solutions with maximum gradient magnitudes up to $10^4$ and minimum mesh sizes of $10^{−5}.$ We investigate the self-similar patterns and blowup rates of these solutions, and validate our numerical findings by comparing them to established analytical results from a recent study.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-322.250224
East Asian Journal on Applied Mathematics, Vol. 14 (2024), Iss. 3 : pp. 601–635
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Landau-Lifshitz-Gilbert equation adaptive mesh blowup solution.