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Volume 14, Issue 3
An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation

Zheyue Fang & Xiaoping Wang

East Asian J. Appl. Math., 14 (2024), pp. 601-635.

Published online: 2024-05

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  • 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.

  • AMS Subject Headings

35Q60, 35B44, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-601, author = {Fang , Zheyue and Wang , Xiaoping}, title = {An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-322.250224}, url = {http://global-sci.org/intro/article_detail/eajam/23163.html} }
TY - JOUR T1 - An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation AU - Fang , Zheyue AU - Wang , Xiaoping JO - East Asian Journal on Applied Mathematics VL - 3 SP - 601 EP - 635 PY - 2024 DA - 2024/05 SN - 14 DO - http://doi.org/10.4208/eajam.2023-322.250224 UR - https://global-sci.org/intro/article_detail/eajam/23163.html KW - Landau-Lifshitz-Gilbert equation, adaptive mesh, blowup solution. AB -

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.

Fang , Zheyue and Wang , Xiaoping. (2024). An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation. East Asian Journal on Applied Mathematics. 14 (3). 601-635. doi:10.4208/eajam.2023-322.250224
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