Force-gradient nested multirate methods for Hamiltonian systems

Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential can be exploited by coupling force-gradient decomposition methods with splitting techniques for multi-time scale problems to further increase the accuracy of the scheme and reduce the computational costs. In this paper, we derive novel force-gradient nested methods and test them numerically. We apply them on the three-body problem, modified for a better observation of the advantageous properties, needed for the future research.