The stochastic Landau-Lifshitz-Gilbert (SLLG) equation describes the magnetisation of a ferromagnetic material, where the magnetisation direction is subject to thermal fluctuations.
Given a complete, filtered probability space, we consider an ensemble of N interacting magnetic spins with a Hamiltonian consisting of three energy terms. The stochastic noise is interpreted in the Stratonovich sense.
An important requirement for a successful numerical treatment is that a chosen numerical method respects the qualitative behaviour of the SLLG, e.g., for each spin, the solution trajectory evolves on the unit sphere.
In this talk we will discuss splitting approaches, where we decompose the equation into linear and non-linear deterministic subsystems, which can be solved either exactly or approximately via the Cayley-transform, and linear stochastic subsystems, which we approximate with methods based on the Magnus expansion. The composition of these flows yields a flexible integrator with favourable geometric properties under reasonable computational cost.