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Title: A fast multipole method for stellar dynamics
Authors: Dehnen, Walter
First Published: 11-Sep-2014
Publisher: Springer
Citation: Computational Astrophysics and Cosmology, 2014, 1 : 1.
Abstract: The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than O(N) operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of ~ 10⁻⁷, the computational costs exhibit an empirical scaling of ∝ N^{0.87}. My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for N ≳ 10⁵.
DOI Link: 10.1186/s40668-014-0001-7
ISSN: 2197-7909
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the author, 2014. This is an open-access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, Dept. of Physics and Astronomy

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