Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems

Abstract

We discuss two physical systems from separate disci- plines that make use of the same algorithmic and math- ematical structures to reduce the number of operations necessary to complete a realistic simulation. In the grav- itational N-body problem, the acceleration of an object is given by the familiar Netwonian laws of motion and gravitation. The computational load is reduced by treating groups of bodies as single multipole sources rather than in- dividual bodies. In the simulation of incompressible flows, the flow may be modeled by the dynamics of a set of interacting vortices. Vortices are vector objects in three di- mensions, but their interactions are mathematically simil ar to that of gravitating masses. The multipole approximation can be used to greatly reduce the time needed to compute the interactions between vortices. Both types of simulations were carried out on the Intel Touchstone Delta, a parallel MIMD computer with 512 processors. Timings are reported for systems of up to 10 million bodies, and demonstrate that the implementation scales well on massively parallel systems. The majority of the code is common between the two applications, which differ only in certain "physics" modules. In particular, th e code for parallel tree construction and traversal is shared .