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Force-gradient decomposition methods are used to improve the energypreservation of symplectic schemes applied to Hamiltonian systems. If thepotential is composed of different parts with strongly varying dynamics, thismultirate potential can be exploited by coupling force-gradient decompositionmethods with splitting techniques for multi-time scale problems to furtherincrease the accuracy of the scheme and reduce the computational costs. In thispaper, we derive novel force-gradient nested methods and test them numerically.Such methods can be used to increase the acceptance rate for the moleculardynamics step of the Hybrid Monte Carlo algorithm (HMC) and hence improve itscomputational efficiency.

Force-Gradient Nested Multirate Methods for Hamiltonian System