Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques
Analysis of PDEs
2024-07-16 v1 Numerical Analysis
Numerical Analysis
Abstract
Spin currents act on ferromagnets by exerting a torque on the magnetisation. This torque is modelled by appending additional terms to the Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous Landau-Lifshitz-Gilbert equation. We first prove the existence and uniqueness of high regularity local solutions to this equation using the Faedo-Galerkin method. Then we construct a numerical method for the problem and prove that it converges to a global weak solution of the PDE. Numerical simulations of the problem are also included.
Keywords
Cite
@article{arxiv.2407.10429,
title = {Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques},
author = {Noah Vinod and Thanh Tran},
journal= {arXiv preprint arXiv:2407.10429},
year = {2024}
}