Holomorphic regularity and approximation of the stochastic Landau-Lifshitz-Gilbert equation

Abstract

The Doss--Sussmann transformation reformulates the stochastic Landau-Lifshitz-Gilbert (LLG) equation into a PDE with random coefficients. These coefficients can be parametrised, resulting in a parametric PDE with possibly infinitely many parameters. Holomorphic regularity of the solution with respect to these parameters is established and exploited in convergence analysis of the approximation in the parameter direction. Together with the usual finite-element approximation in the spatial direction, this yields an efficient numerical solution to the LLG equation. This is a joint work with Xin An and Josef Dick at UNSW, and with Michael Feischl and Andrea Scaglioni at TU Wien.