Communication-Optimal Parallel N-body Solvers

We present new analysis, algorithmic techniques, and implementations of the Fast Multipole Method (FMM) for solving N-body problems. Our research specifically addresses two key challenges. The first challenge is how to engineer fast code for today's platforms. We present the first in-depth study of multicore optimizations and tuning for FMM, along with a systematic approach for transforming a conventionally parallelized FMM into a highly-tuned one. We introduce novel optimizations that significantly improve the within-node scalability of the FMM, thereby enabling high-performance in the face of multicore and many core systems. The second challenge is how to understand scalability on future systems. We present a new algorithmic complexity analysis of the FMM that considers both intra- and inter-node communication costs. This analysis yields the surprising prediction that although the FMM is largely compute-bound today, and therefore highly scalable on current systems, the trajectory of processor architecture designs-if there are no significant change-could cause it to become communication-bound as early as the year 2020. This prediction suggests the utility of our analysis approach, which directly relates algorithmic and architectural characteristics, for enabling a new kind of high-level algorithm-architecture co-design.