The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymplectic PDE, and suggest an efficient symplectic splitting method for time integration. Furthermore we introduce a new space-time box scheme discretization which satisfies a discrete local conservation law for energy flow, implicit in the LLE, and made transparent by the multisymplectic framework.

Hamiltonian systems including symplectic integrators (msc 65P10), None of the above, but in MSC2010 section 70Hxx (msc 70H99), Magnetic materials (msc 82D40)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Frank, J.E. (2003). Geometric space-time integration of ferromagnetic materials. Modelling, Analysis and Simulation [MAS]. CWI.