Fast Fourier Transform Accelerated Fast Multipole Algorithm

Elliott, William D.; Board, John A.

doi:10.1137/s1064827594264259

Cited by 74 publications

(60 citation statements)

References 11 publications

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“…Yarvin and Rokhlin [62] present a generalization of the 1D-FMM applicable to Alpert and Jakob-Chien's interpolation algorithm. See also [25,61]. Finally a backward FFT is performed on φ.…”

Section: Possible Approachesmentioning

confidence: 99%

The Fast Multipole Method: Numerical Implementation

Darve¹

2000

Journal of Computational Physics

307

296

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We study integral methods applied to the resolution of the Maxwell equations where the linear system is solved using an iterative method which requires only matrix-vector products. The fast multipole method (FMM) is one of the most efficient methods used to perform matrix-vector products and accelerate the resolution of the linear system. A problem involving N degrees of freedom may be solved in CN iter N log N floating operations, where C is a constant depending on the implementation of the method. In this article several techniques allowing one to reduce the constant C are analyzed. This reduction implies a lower total CPU time and a larger range of application of the FMM. In particular, new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms. Several numerical tests are also described. These confirm the efficiency and the theoretical complexity of the FMM.

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“…Yarvin and Rokhlin [62] present a generalization of the 1D-FMM applicable to Alpert and Jakob-Chien's interpolation algorithm. See also [25,61]. Finally a backward FFT is performed on φ.…”

Section: Possible Approachesmentioning

confidence: 99%

The Fast Multipole Method: Numerical Implementation

Darve¹

2000

Journal of Computational Physics

307

296

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“…Elliott & Board (1996) successfully reduced the calculation cost in FMM from O(p 4 N) to O(p(log p) 1/2 N) by using a fast fourier transformation and optimal choice of the tree level. Dehnen (2000) proposed a Cartesian FMM, however, its calculation cost is estimated as O(p 6 N).…”

Section: Higher Order Expansion and Application To Fmmmentioning

confidence: 99%

“…Dehnen (2000) proposed a Cartesian FMM, however, its calculation cost is estimated as O(p 6 N). Again this cost can be reduced to O(p 3/2 (log p) 1/2 N) by following Elliott & Board (1996).…”

Section: Higher Order Expansion and Application To Fmmmentioning

confidence: 99%

A natural symmetrization for the plummer potential

Saitoh

Makino

2012

New Astronomy

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“…The FFT acceleration technique used here is basically the one proposed by Elliott and Board (1996), except the block decomposition has been dropped, and scaling of multipole coefficients has been introduced, which is schematically represented on Figure 2. Here the approach will be briefly outlined.…”

Section: Fft Accelerationmentioning

confidence: 99%

Automatic Generation of FFT for Translations of Multipole Expansions in Spherical Harmonics

Kurzak

Mirković

Pettitt

et al. 2008

The International Journal of High Performance Computing Applica

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The fast multipole method (FMM) is an efficient algorithm for calculating electrostatic interactions in molecular simulations and a promising alternative to Ewald summation methods. Translation of multipole expansion in spherical harmonics is the most important operation of the fast multipole method and the fast Fourier transform (FFT) acceleration of this operation is among the fastest methods of improving its performance. The technique relies on highly optimized implementation of fast Fourier transform routines for the desired expansion sizes, which need to incorporate the knowledge of symmetries and zero elements in the input arrays. Here a method is presented for automatic generation of such, highly optimized, routines.

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Fast Fourier Transform Accelerated Fast Multipole Algorithm

Cited by 74 publications

References 11 publications

The Fast Multipole Method: Numerical Implementation

The Fast Multipole Method: Numerical Implementation

A natural symmetrization for the plummer potential

Automatic Generation of FFT for Translations of Multipole Expansions in Spherical Harmonics

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