Volume 20, Issue 2
RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions

Bo Zhang, Jingfang Huang, Nikos P. Pitsianis & Xiaobai Sun

Commun. Comput. Phys., 20 (2016), pp. 534-550.

Published online: 2018-04

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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, neither 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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@Article{CiCP-20-534, author = {}, title = {RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {2}, pages = {534--550}, 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, neither 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.230216.140416sw}, url = {http://global-sci.org/intro/article_detail/cicp/11163.html} }
TY - JOUR T1 - RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions JO - Communications in Computational Physics VL - 2 SP - 534 EP - 550 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.230216.140416sw UR - https://global-sci.org/intro/article_detail/cicp/11163.html KW - AB -

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, neither 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.

Bo Zhang, Jingfang Huang, Nikos P. Pitsianis & Xiaobai Sun. (2020). RECFMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions. Communications in Computational Physics. 20 (2). 534-550. doi:10.4208/cicp.230216.140416sw
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