A parallel adaptive fast multipole method

Abstract

We present parallel versions of a representative N-body application that uses Greengard and Rokhlin's adaptive Fast Multipole Method (FMMJ While parallel implementations of the umform FMM are straightforward and have been developed on alfferent architectures, the aalzptive version complicates the task of obtaining eflective parallel peflormance owing to the nonunz~onn and dynamically changing nature of the problem &mains to which it is applied.We propose and evaluate two techniques for providing load balancing and data locality, both of which take advantage of key insights into the method and its typical applications.Using the better of these techm"ques, we demonstrate 45-fold speedups on galactic sinudations on a 48-processor Stanford DASH machine, a state-of-the-art shared address space multiprocessor even for relatively small problems.We also show good speedups on a 2-ring Kendall Square Research KSR-I. Finally we summarize some key architectural implications of this important computational method.

Fast multipole methods on graphics processors

“…The idea to parallelize the FMM is not new and there are publications that address some basic issues [9,19,20,21,24]. However these publications are mostly related to the development of more coarse-grained parallel algorithms.…”

High performance Fortran for highly irregular problems

“…To our knowledge, the only parallel implementation of this type of method prior to ours is a shared-memory implementation of a 2-D version of the Greengard-Rokhlin method [25]. In previous work [13,14], we have shown that efficient scalable code can be produced in data parallel languages for nonadaptive versions of Anderson's method.…”

Scalable fast multipole methods on distributed heterogeneous architectures

“…On modern multicore and GPU architectures, this requires parallelization of the algorithm. The FMM has been sought to be parallelized almost since its invention -see e.g., [5,6,7,8]. However, these works are mostly related to more coarse-grained parallel algorithms and often focus on tree codes rather than the FMM.…”