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    Fourier-Based Fast Multipole Method for the Helmholtz Equation

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    Type
    Article
    Authors
    Cecka, Cris
    Darve, Eric
    Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/598360
    
    Metadata
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    Abstract
    The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
    Citation
    Cecka C, Darve E (2013) Fourier-Based Fast Multipole Method for the Helmholtz Equation. SIAM Journal on Scientific Computing 35: A79–A103. Available: http://dx.doi.org/10.1137/11085774X.
    Sponsors
    This research was supported by the U.S. Army Research Laboratory, through the Army HighPerformance Computing Research Center, Cooperative Agreement W911NF-07-0027, the StanfordSchool of Engineering, and the King Abdullah University of Science and Technology.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/11085774X
    ae974a485f413a2113503eed53cd6c53
    10.1137/11085774X
    Scopus Count
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