FAST PARALLEL TREE CODES FOR GRAVITATIONAL AND FLUID DYNAMICAL N-BODYPROBLEMS

We discuss two physical systems from different disciplines that make u se of the same algorithmic and mathematical structures as a way of red ucing the number of operations necessary to complete a realistic simul ation. In the gravitational N-body problem, the acceleration of an obj ect is given by the familiar Newtonian laws Of motion and gravitation. The computational load is reduced by treating groups of bodies as sin gle multipole sources rather than as individual bodies. In the simulat ion of incompressible flows, the flow may be modeled by the dynamics o f a set of N interacting vortices. Vortices are vector objects in thre e dimensions, but their interactions are mathematically similar to tha t of gravitating masses. The multipole approximation can be used to gr eatly reduce the time needed to compute the interactions between vorti ces. Both types of simulations are carried out on the Intel TouchStone Delta, a parallel MIMD computer with 512 processors. Timings are repo rted 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 to both applications, which differ only in some of the ''physics'' modules. In particular, the code for parallel-tree construction and traversal is shared.