Splitting Integrators for the Stochastic Landau--Lifshitz Equation | Zendy

M. Ableidinger | Zendy; Evelyn Buckwar | Zendy

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Splitting Integrators for the Stochastic Landau--Lifshitz Equation

Author(s) -

M. Ableidinger,

Evelyn Buckwar

Publication year - 2016

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/15m103529x

Subject(s) - integrator , mathematics , landau–lifshitz–gilbert equation , nonlinear system , hamiltonian (control theory) , convergence (economics) , variational integrator , dimension (graph theory) , mathematical analysis , statistical physics , magnetization , mathematical optimization , physics , quantum mechanics , pure mathematics , magnetic field , voltage , economics , economic growth

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.

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