Collective Symplectic Integrators on $S_2^N \times T^*\mathbb{R}^M$
arXiv:1809.06231
Originality Incremental advance
AI Analysis
This work provides a new numerical method for simulating Hamiltonian systems on a specific product manifold, which is incremental for the field of geometric numerical integration.
The paper develops a novel symplectic integrator for Hamiltonian systems on the product manifold $S_2^n \ imes T^*\\mathbb{R}^m$, deriving algebraic conditions for symplecticity of partitioned Runge-Kutta methods on such manifolds.
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically, algebraic conditions for their symplecticity are derived.