  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.
