The Tree Particle‐Mesh N ‐Body Gravity Solver

The Tree-Particle-Mesh (TPM) N-body algorithm couples the tree algorithm fordirectly computing forces on particles in an hierarchical grouping scheme withthe extremely efficient mesh based PM structured approach. The combined TPMalgorithm takes advantage of the fact that gravitational forces are linearfunctions of the density field. Thus one can use domain decomposition to breakdown the density field into many separate high density regions containing asignificant fraction of the mass but residing in a very small fraction of thetotal volume. In each of these high density regions the gravitational potentialis computed via the tree algorithm supplemented by tidal forces from theexternal density distribution. For the bulk of the volume, forces are computedvia the PM algorithm; timesteps in this PM component are large compared toindividually determined timesteps in the tree regions. Since each tree regioncan be treated independently, the algorithm lends itself to very efficientparallelization using message passing. We have tested the new TPM algorithm (arefinement of that originated by Xu 1995) by comparison with results fromFerrell & Bertschinger's P^3M code and find that, except in small clusters, theTPM results are at least as accurate as those obtained with thewell-established P^3M algorithm, while taking significantly less computingtime. Production runs of 10^9 particles indicate that the new code has greatscientific potential when used with distributed computing resources.Comment: 24 pages including 9 figures, uses aaspp4.sty; revised to match published versio