The Tree-Particle-Mesh N-body Gravity Solver

Abstract

The Tree-Particle-Mesh (TPM) N-body algorithm couples the tree algorithm for directly computing forces on particles in an hierarchical grouping scheme with the extremely efficient mesh based PM structured approach. The combined TPM algorithm takes advantage of the fact that gravitational forces are linear functions of the density field. Thus one can use domain decomposition to break down the density field into many separate high density regions containing a significant fraction of the mass but residing in a very small fraction of the total volume. In each of these high density regions the gravitational potential is computed via the tree algorithm supplemented by tidal forces from the external density distribution. For the bulk of the volume, forces are computed via the PM algorithm; timesteps in this PM component are large compared to individually determined timesteps in the tree regions. Since each tree region can be treated independently, the algorithm lends itself to very efficient parallelization using message passing. We have tested the new TPM algorithm (a refinement of that originated by Xu 1995) by comparison with results from Ferrell & Bertschinger's P^3M code and find that, except in small clusters, the TPM results are at least as accurate as those obtained with the well-established P^3M algorithm, while taking significantly less computing time. Production runs of 10^9 particles indicate that the new code has great scientific potential when used with distributed computing resources.