An Efficient Load Balancing Technique for Parallel FMA in Message Passing Environment

The N-body simulation has been used extensively in study of the dynamics of galactic systems, uid, and biomolecules. It is known to be computational bound due to direct force calculation among bodies in the system. The time complexity is O(N 2) where N is the number of bodies. Fast multipole algorithm, proposed by Greengard and Rokhlin, reduces the complexity to O(N). Tremendous amount of work had been devoted to parallelization of fast multipole algorithm for uniformly distributed particles. However, the particles in many applications are distributed non-uniformly. This poses the problem of load imbalancing among processors which, in turn increases total computational cost. Existing partitioning techniques do not work well due to the tight relationship in the translations of multipole and local expansions when applying to parallel fast multipole algorithm in message passing environment. In this paper, we propose a new partitioning technique called weighted subtrees and present its performance results.