An efficient multiple time-scale reversible integrator for the gravitational N-body problem

A large gravitational (or classical atomic) N-body simulation typically includes fast binary stars, planet-moon systems, or other tightly bound objects, demanding a small timestep and effectively limiting the time interval over which simulation can take place. While ad-hoc averaging schemes have been used before, these are generally neither symplectic nor reversible, impairing their long time-interval stability properties. In this article, we describe the design of a powerful reversible integrator based on partitioning, averaging, reversible adaptive timestepping, and smooth force decomposition. This method also incorporates a modification of the reversible averaging method of [J. Comput. Phys. 171 (2001) 95] based on an interpolation of the forces acting on the fast variables which is potentially much more efficient than the original method. (C) 2002 IMACS. Published by Elsevier Science B.V. All. rights reserved.