Scalable Distributed Fast Multipole Methods

Abstract

Abstract-The Fast Multipole Method (FMM) allows O(N ) evaluation to any arbitrary precision of N -body interactions that arises in many scientific contexts. These methods have been parallelized, with a recent set of papers attempting to parallelize them on heterogeneous CPU/GPU architectures [1]. While impressive performance was reported, the algorithms did not demonstrate complete weak or strong scalability. Further, the algorithms were not demonstrated on nonuniform distributions of particles that arise in practice. In this paper, we develop an efficient scalable version of the FMM that can be scaled well on many heterogeneous nodes for nonuniform data. Key contributions of our work are data structures that allow uniform work distribution over multiple computing nodes, and that minimize the communication cost. These new data structures are computed using a parallel algorithm, and only require a small additional computation overhead. Numerical simulations on a heterogeneous cluster empirically demonstrate the performance of our algorithm.

Abstract: Scalable Fast Multipole Methods for Vortex Element Methods

“…We develop new data structures for the distributed algorithm which separate the computation and communication to avoid synchronization during GPU computations. The new data structures [7] build on the local essential tree (LET) [8], [9] concept but use a master-slave model and further have a novel parallel construction algorithm, in which the granularity is at the level of the spatial boxes (which allows finer parallelization than at the single-node level). Basically, each node divides its assigned domain into small spatial boxes via octrees and classifies each box into one of five categories in parallel.…”

Highly parallel boundary element method for solving extremely large, wide-area power-line models

“…Therefore, we sought to extend our software to run on multiple nodes. There has been a lot of work done on parallelizing the FMM across many nodes (Hu et al, 2011, 2012; Lashuk et al, 2012), especially with regard to maintaining good strong and weak scaling. In many cases, multi-node FMM algorithms have been applied to the BEM (Dang et al, 2016; Malhotra and Biros, 2016; Michiels et al, 2015; Yokota et al, 2011).…”

GPU accelerated fast multipole boundary element method for simulation of 3D bubble dynamics in potential flow

“…The FMM can be efficiently parallelized [37]. The first implementation of the FMM on graphics processors [32] was developed further [38,39], where the FMM was implemented on heterogeneous computing architectures consisting of multicore CPUs and GPUs. This FMM parallelization strategy for heterogeneous architectures was successfully used in fluid and molecular dynamics [40,41,42,43,44] and in electro-and magnetostatics [45].…”