A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise
Numerical Analysis
2017-03-20 v1
Abstract
We propose an unconditionally convergent linear finite element scheme for the stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional noise. By using the Doss-Sussmann technique, we first transform the stochastic LLG equation into a partial differential equation that depends on the solution of the auxiliary equation for the diffusion part. The resulting equation has solutions absolutely continuous with respect to time. We then propose a convergent -linear scheme for the numerical solution of the reformulated equation. As a consequence, we are able to show the existence of weak martingale solutions to the stochastic LLG equation.
Keywords
Cite
@article{arxiv.1703.05901,
title = {A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise},
author = {Beniamin Goldys and Joseph Grotowski and Kim-Ngan Le},
journal= {arXiv preprint arXiv:1703.05901},
year = {2017}
}