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    Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation

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    Type
    Conference Paper
    Authors
    Yokota, Rio cc
    Ibeid, Huda cc
    Keyes, David E. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Applied Mathematics and Computational Science Program
    Extreme Computing Research Center
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2017-10-04
    Online Publication Date
    2017-10-04
    Print Publication Date
    2017
    Permanent link to this record
    http://hdl.handle.net/10754/627144
    
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    Abstract
    There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
    Citation
    Yokota R, Ibeid H, Keyes D (2017) Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation. Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing: 267–286. Available: http://dx.doi.org/10.1007/978-3-319-62426-6_17.
    Sponsors
    We thank François-Henry Rouet, Pieter Ghysels, and Xiaoye, S. Li for providing the STRUMPACK interface for our comparisons between FMM and HSS. This work was supported by JSPS KAKENHI Grant-in-Aid for Research Activity Start-up Grant Number 15H06196. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.
    Publisher
    Springer Nature
    Journal
    Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing
    Conference/Event name
    1st InternationalWorkshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, EPASA 2015
    DOI
    10.1007/978-3-319-62426-6_17
    arXiv
    1602.02244
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-62426-6_17
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-62426-6_17
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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