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 - <p style="text-align: justify;">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.</p>