Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Comparison of the Efficiency of Translation Operators Used in the Fast Multipole Method for the 3D Laplace Equation

    Thumbnail
    View/Open
    LaplaceTranslation_CSTR_4701.pdf (783.2Kb)
    No. of downloads: 808

    Date
    2005-11-30
    Author
    Gumerov, Nail A.
    Duraiswami, Ramani
    Metadata
    Show full item record
    Abstract
    We examine the practical implementation of a fast multipole method algorithm for the rapid summation of Laplace multipoles. Several translation operators with different asymptotic computational and memory complexities have been proposed for this problem. These algorithms include: Method 0 — the originally proposed matrix based translations due to Greengard and Rokhlin (1987), Method 1 — the rotation, axial translation and rotation algorithm due to White and Martin Head-Gordon (1993), and Method 3 — the plane-wave version of the multipole-to local translation operator due to Greengard and Rokhlin (1997). We compare the algorithms on data sets of varying size and with varying imposed accuracy requirements. While from the literature it would have been expected that method 2 would always be the method of choice, at least as far as computational speed is concerned, we find that this is not always the case. We find that as far as speed is concerned the choice between methods 1 and 2 depends on problem size and error requirements. Method 2 is the algorithm of choice for large problems where high accuracy is required, though the advantage is not clear cut, especially if memory requirements are an issue. If memory is an issue, Method 1 is the method of choice for most problems. A new analysis of the computational complexities of the algorithms is provided, which explains the observed results. We provide guidelines for choosing parameters for FMM algorithms.
    URI
    http://hdl.handle.net/1903/3023
    Collections
    • Technical Reports from UMIACS
    • Technical Reports of the Computer Science Department

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility