Splitting Integrators for the Stochastic Landau–Lifshitz Equation

In this article we construct splitting integrators for a finite-dimensional version of the stochastic Landau–Lifshitz equation under the influence of global and local energy terms. The methods preserve the length of the magnetization spins exactly and reproduce the energy evolution of the equation. Depending on the structure of the Hamiltonian, the methods either are explicit or contain nonlinear subsystems of small dimension, which leads to a smaller computational cost compared with standard implicit integrators. Numerical simulations are provided for evidencing convergence order and long-time behavior of the constructed methods.