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RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions

Published online by Cambridge University Press:  21 July 2016

Bo Zhang
Affiliation:
Center for Research in Extreme Scale Technologies, Indiana University, Bloomington, IN, 47404, USA
Jingfang Huang
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599, USA
Nikos P. Pitsianis
Affiliation:
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, GR-54124, Greece Department of Computer Science, Duke University, Durham, NC, 27708, USA
Xiaobai Sun
Affiliation:
Department of Computer Science, Duke University, Durham, NC, 27708, USA
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Abstract

We 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.

Type
Computational Software
Copyright
Copyright © Global-Science Press 2016 

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References

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RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions
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