GROMMET: an N-body code for high-resolution simulations of individual galaxies

Abstract

This paper presents a fast, economical particle‐multiple‐mesh N‐body code optimized for large‐N modelling of collisionless dynamical processes, such as black hole wandering or bar–halo interactions, occurring within isolated galaxies. The code has been specially designed to conserve linear momentum. Despite this, it also has variable softening and an efficient block‐time‐step scheme: the force between any pair of particles is calculated using the finest mesh that encloses them both (respecting Newton's third law) and is updated only on the longest time‐step of the two (which conserves momentum). For realistic galaxy models with N≳ 106, it is faster than the fastest comparable tree code by factors ranging from ∼2 (using single time‐steps) to ∼10 (multiple time‐steps in a concentrated galaxy).

Actions, angles and frequencies for numerically integrated orbits

“…Rather at some time t the potential should be computed on a spatial grid (e.g. Magorrian 2007), and the equations of motion in this potential should be integrated for NT timesteps starting from the phasespace location of each particle at time t. These integrations in a fixed potential lend themselves to massive parallelization, for example on a Graphical Processor Unit (GPU) so it should be possible to compute angle-action coordinates for very large numbers of particles .…”

N-body integrators with individual time steps from Hierarchical splitting

“…These integrators are remarkably simple and closely follow previous work: specifically they can be seen as a generalization of the scheme used in the mesh-based integrator for collision-less systems GROMMET (Magorrian, 2007) and are closely related to the Hamiltonian splitting methods used in planetary dynamics (Duncan et al, 1998;Saha and Tremaine, 1994) or the force splitting methods used in molecular dynamics (e.g. Tuckerman et al, 1992).…”

“…The bin in which a particle resides determines the frequency of force evaluations and each successively higher bin has a factor 2 smaller interval between updates. This block time step scheme has been adopted in a wide range of codes, in for example codes for galactic simulations (Dubinski, 1996;Magorrian, 2007), cosmological simulations (Stadel, 2001), Smooth Particle Hydrodynamics codes (Springel, 2005;Wadsley et al, 2004) and also modern Hermite integrators for collisional stellar systems (Makino, 1991;Aarseth, 1999;Portegies Zwart et al, 2001;Harfst et al, 2008;Konstantinidis and Kokkotas, 2010). The popularity of this scheme stems from the fact that it allows for individual tailored time steps while still grouping particles with similar time steps together -which means that the cost of synchronizing the rest of the system is shared by all the particles in a given bin and parallelization of the force calculation is possible.…”

N-body simulations of gravitational dynamics

“…The periodic boundary conditions can be avoided either by simply doubling the computational domain in each dimension or better by James' [145] method, which subtracts the contributions from the periodic replicas of the computational box via a Fourier technique involving surface charges. Combining this with a set of nested grids of increasing resolution enables an efficient FFT-based force solver for inhomogeneous single stellar systems, such as galaxies [146].…”