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

Part of: Other generalizations Basic linear algebra

Published online by Cambridge University Press:  21 July 2016

Bo Zhang ,
Jingfang Huang ,
Nikos P. Pitsianis  and
Xiaobai Sun
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
*
*Corresponding author. Email addresses:[email protected] (B. Zhang), [email protected] (J. Huang), [email protected] (N. P. Pitsianis), [email protected] (X. Sun)
*Corresponding author. Email addresses:[email protected] (B. Zhang), [email protected] (J. Huang), [email protected] (N. P. Pitsianis), [email protected] (X. Sun)
*Corresponding author. Email addresses:[email protected] (B. Zhang), [email protected] (J. Huang), [email protected] (N. P. Pitsianis), [email protected] (X. Sun)
*Corresponding author. Email addresses:[email protected] (B. Zhang), [email protected] (J. Huang), [email protected] (N. P. Pitsianis), [email protected] (X. Sun)
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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.

Keywords

Fast multipole methodrecursive parallelizationdynamic schedulingCoulomb interactionscreened Coulomb interaction

MSC classification

Secondary: 15A06: Linear equations 31C20: Discrete potential theory and numerical methods
Type
Computational Software
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 534 - 550
Copyright
Copyright © Global-Science Press 2016 

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References

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