Seminar Computational and Applied Mathematics

Abstract:We present a novel structure preserving numerical method for Lie-Poisson systems on the dual of semidirect product Lie algebras. The method fully preserves the underlying geometry, namely the Lie-Poisson structure and all the Casimirs, and nearly preserves the Hamiltonian function. We illustrate the method on two models describing the motion of magnetic fluids, the equations of incompressible magnetohydrodynamics, and the Alfvén wave turbulence equations. For the latter case, we reveal the formation of large scale quasi-periodic vortex blob dynamics.

This is a joint work with Klas Modin.