#### Conference abstracts

Session A5 - Geometric Integration and Computational Mechanics

July 10, 17:00 ~ 17:30

## The spherical midpoint method

### Klas Modin

### 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).