Assessing the Hierarchical Hamiltonian Splitting Integrator for
  Collisionless N-body Simulations
  The N-body problem has become one of the hottest topics in the fields of
computational dynamics and cosmology. The large dynamical range in some
astrophysical problems led to the use of adaptive time steps to integrate
particle trajectories, however, the search of optimal strategies is still
challenging. We quantify the performance of the hierarchical time step
integrator Hamiltonian Splitting (HamSp) for collisionless multistep
simulations. We compare with the constant step Leap-Frog (LeapF) integrator and
the adaptive one (AKDK). Additionally, we explore the impact of different time
step assigning functions. There is a computational overhead in HamSp however
there are two interesting advantages: choosing a convenient time-step function
may compensate and even turn around the efficiency compared with AKDK. We test
both reversibility and time symmetry. The symmetrized nature of the HamSp
integration is able to provide time-reversible integration for medium time
scales and overall deliver better energy conservation for long integration
times, and the linear and angular momentum are preserved at machine precision.
We address the impact of using different integrators in astrophysical systems.
We found that in most situations both AKDK and HamSp are able to correctly
simulate the problems. We conclude that HamSp is an attractive and competitive
alternative to AKDK, with, in some cases, faster and with better energy and
momentum conservation. The use of recently discussed Bridge splitting
techniques with HamSp may allow to reach considerably high efficiency.
