An Adaptive Moving Mesh Method for Simulating Finite-Time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation

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.