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Title: Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

Abstract

I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.

Authors:
 [1]
  1. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1545079
Report Number(s):
arXiv:1906.10734; FERMILAB-PUB-19-277-A
Journal ID: ISSN 1538-4365; 1741462
Grant/Contract Number:  
AC02-07CH11359
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal. Supplement Series (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal. Supplement Series (Online); Journal Volume: 243; Journal Issue: 2; Journal ID: ISSN 1538-4365
Publisher:
American Astronomical Society/IOP
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; methods: numerical

Citation Formats

Gnedin, Nickolay Y. Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method. United States: N. p., 2019. Web. https://doi.org/10.3847/1538-4365/ab2d24.
Gnedin, Nickolay Y. Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method. United States. https://doi.org/10.3847/1538-4365/ab2d24
Gnedin, Nickolay Y. Tue . "Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method". United States. https://doi.org/10.3847/1538-4365/ab2d24. https://www.osti.gov/servlets/purl/1545079.
@article{osti_1545079,
title = {Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method},
author = {Gnedin, Nickolay Y.},
abstractNote = {I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.},
doi = {10.3847/1538-4365/ab2d24},
journal = {The Astrophysical Journal. Supplement Series (Online)},
number = 2,
volume = 243,
place = {United States},
year = {2019},
month = {7}
}

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