Removing the Barrier to Scalability in Parallel FMM

TL;DR

This paper proposes a technique to eliminate scalability bottlenecks in the Fast Multipole Method by overlapping computations, enabling more efficient parallel processing for large-scale problems.

Contribution

It introduces a novel overlapping strategy that removes the workload bottleneck at higher FMM tree levels, improving parallel scalability.

Findings

Eliminates the bottleneck caused by decreasing workload at higher levels.

Demonstrates improved parallel scalability through overlapping computations.

Applicable to large-scale FMM implementations.

Abstract

The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be eliminated by overlapping multipole and local expansion computations with direct kernel evaluations on the finest level grid.