  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.
Such methods can be used to increase the acceptance rate for the molecular
dynamics step of the Hybrid Monte Carlo algorithm (HMC) and hence improve its
computational efficiency.
