Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 10, 17:00 ~ 17:30

The spherical midpoint method

Chalmers and University of Gothenburg, Sweden   -   klas.modin@chalmers.se

The 2-sphere $S^2$ is, perhaps, the most fundamental example of a non-canonical symplectic manifold. Yet, to construct symplectic integration schemes for Hamiltonian systems on $S^2$ has been surprisingly cumbersome. In this talk I shall present a new integrator---the spherical midpoint method---for general Hamiltonian systems on $S^2$. The new method uses a minimal number of variables, is equivariant with respect to the homogeneous space structure of the 2-sphere, and is readily extendable to general Hamiltonian systems on $(S^2)^m\times \mathbb{R}^{2n}$. I shall also discuss applications to atomistic spin dynamics in condensed matter physics (collaboration with physicists at Uppsala University), and a possible generalization of the method to other Kähler manifolds.

Joint work with Robert McLachlan (Massey University, New Zealand) and Olivier Verdier (Western Norway University of Applied Sciences).

FoCM 2017, based on a nodethirtythree design.