ExaFMM: a high-performance fast multipole method library with C++ and Python interfaces

AbstractWe present RECFMM, a program representation and implementation of a recursive scheme for parallelizing the adaptive fast multipole method (FMM) on shared-memory computers. It achieves remarkable high performance while maintaining mathematical clarity and flexibility. The parallelization scheme signifies the recursion feature that is intrinsic to the FMM but was not well exploited. The program modules of RECFMM constitute a map between numerical computation components and advanced architecture mechanisms. The mathematical structure is preserved and exploited, not obscured nor compromised, by parallel rendition of the recursion scheme. Modern software system—CILK in particular, which provides graph-theoretic optimal scheduling in adaptation to the dynamics in parallel execution—is employed. RECFMM supports multiple algorithm variants that mark the major advances with low-frequency interaction kernels, and includes the asymmetrical version where the source particle ensemble is not necessarily the same as the target particle ensemble. We demonstrate parallel performance with Coulomb and screened Coulomb interactions.

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PARALLELIZATION OF FAST MULTIPOLE METHOD USING MPI ON IBM HIGH PERFORMANCE COMPUTERS

Recent Advances in Computational Science and Engineering ◽

10.1142/9781860949524_0091 ◽

2002 ◽

Author(s):

FANG WU ◽

YAOJIANG ZHANG ◽

CHAN PING EDWIN LIM ◽

ERPING LI

Keyword(s):

High Performance ◽

Fast Multipole Method ◽

Fast Multipole ◽

Multipole Method ◽

High Performance Computers

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A Parallel Adaptive Fast Multipole Method for High Performance Vortex Method Based Simulations

10.1115/imece1999-1245 ◽

1999 ◽

Author(s):

James P. Collins ◽

Athanassios A. Dimas ◽

Peter S. Bernard

Keyword(s):

Turbulent Flows ◽

High Performance ◽

Message Passing Interface ◽

Parallel Implementation ◽

Fast Multipole Method ◽

Vortex Method ◽

Vortex Filament ◽

Fast Multipole ◽

Replication Process ◽

Multipole Method

Abstract A fast vortex method for the simulation of turbulent flows based on a parallel implementation of the Fast Multipole Method (FMM) is presented. The vortex method includes a hybrid vortex filament/sheet representation of the flow field, a vortex filament creation model that imitates the physical vortex self-replication process, and a hairpin removal and reconnection mechanism to limit the number and scale of vortical structures to those that are dynamically essential. The FMM, which is used to reduce the operation count in computing the velocity field, is the main focus of this paper. Two related FMM methods, referred to as the uniform and the adaptive FMM, are described. Both methods are parallelized using the Message Passing Interface (MPI) library, and timings for single and multiple processor calculations are given. Results are presented from a simulation of the flow past a prolate spheroid in a uniform stream at 30° angle of attack.

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