A fast multipole method for stellar dynamics

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 operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to ap...
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Autor*in:	Dehnen, Walter [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	methods: numerical methods: N-body simulations

Anmerkung:	© Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd.

Übergeordnetes Werk:	Enthalten in: Computational Astrophysics and Cosmology - New York, NY [u.a.] : Springer international, 2014, 1(2014), 1 vom: 11. Sept.
Übergeordnetes Werk:	volume:1 ; year:2014 ; number:1 ; day:11 ; month:09

Links:	Volltext

DOI / URN:	10.1186/s40668-014-0001-7

Katalog-ID:	SPR037336940

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allfields	10.1186/s40668-014-0001-7 doi (DE-627)SPR037336940 (SPR)s40668-014-0001-7-e DE-627 ger DE-627 rakwb eng Dehnen, Walter verfasserin aut A fast multipole method for stellar dynamics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd. 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 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 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213 Enthalten in Computational Astrophysics and Cosmology New York, NY [u.a.] : Springer international, 2014 1(2014), 1 vom: 11. Sept. (DE-627)815913885 (DE-600)2806586-4 2197-7909 nnns volume:1 year:2014 number:1 day:11 month:09 https://dx.doi.org/10.1186/s40668-014-0001-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 1 2014 1 11 09
spelling	10.1186/s40668-014-0001-7 doi (DE-627)SPR037336940 (SPR)s40668-014-0001-7-e DE-627 ger DE-627 rakwb eng Dehnen, Walter verfasserin aut A fast multipole method for stellar dynamics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd. 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 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 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213 Enthalten in Computational Astrophysics and Cosmology New York, NY [u.a.] : Springer international, 2014 1(2014), 1 vom: 11. Sept. (DE-627)815913885 (DE-600)2806586-4 2197-7909 nnns volume:1 year:2014 number:1 day:11 month:09 https://dx.doi.org/10.1186/s40668-014-0001-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 1 2014 1 11 09
allfields_unstemmed	10.1186/s40668-014-0001-7 doi (DE-627)SPR037336940 (SPR)s40668-014-0001-7-e DE-627 ger DE-627 rakwb eng Dehnen, Walter verfasserin aut A fast multipole method for stellar dynamics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd. 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 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 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213 Enthalten in Computational Astrophysics and Cosmology New York, NY [u.a.] : Springer international, 2014 1(2014), 1 vom: 11. Sept. (DE-627)815913885 (DE-600)2806586-4 2197-7909 nnns volume:1 year:2014 number:1 day:11 month:09 https://dx.doi.org/10.1186/s40668-014-0001-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 1 2014 1 11 09
allfieldsGer	10.1186/s40668-014-0001-7 doi (DE-627)SPR037336940 (SPR)s40668-014-0001-7-e DE-627 ger DE-627 rakwb eng Dehnen, Walter verfasserin aut A fast multipole method for stellar dynamics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd. 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 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 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213 Enthalten in Computational Astrophysics and Cosmology New York, NY [u.a.] : Springer international, 2014 1(2014), 1 vom: 11. Sept. (DE-627)815913885 (DE-600)2806586-4 2197-7909 nnns volume:1 year:2014 number:1 day:11 month:09 https://dx.doi.org/10.1186/s40668-014-0001-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 1 2014 1 11 09
allfieldsSound	10.1186/s40668-014-0001-7 doi (DE-627)SPR037336940 (SPR)s40668-014-0001-7-e DE-627 ger DE-627 rakwb eng Dehnen, Walter verfasserin aut A fast multipole method for stellar dynamics 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd. 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 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 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213 Enthalten in Computational Astrophysics and Cosmology New York, NY [u.a.] : Springer international, 2014 1(2014), 1 vom: 11. Sept. (DE-627)815913885 (DE-600)2806586-4 2197-7909 nnns volume:1 year:2014 number:1 day:11 month:09 https://dx.doi.org/10.1186/s40668-014-0001-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 1 2014 1 11 09
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author	Dehnen, Walter
spellingShingle	Dehnen, Walter misc methods: numerical misc methods: N-body simulations A fast multipole method for stellar dynamics
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topic_title	A fast multipole method for stellar dynamics methods: numerical (dpeaa)DE-He213 methods: N-body simulations (dpeaa)DE-He213
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title	A fast multipole method for stellar dynamics
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title_full	A fast multipole method for stellar dynamics
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title_sort	fast multipole method for stellar dynamics
title_auth	A fast multipole method for stellar dynamics
abstract	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 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} $, the computational costs exhibit an empirical scaling of . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd.
abstractGer	Abstract The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of ∼$ 10^{−7} $, the computational costs exhibit an empirical scaling of . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd.
abstract_unstemmed	Abstract The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of ∼$ 10^{−7} $, the computational costs exhibit an empirical scaling of . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for . © Dehnen; licensee Springer 2014. This article is published under license to BioMed Central Ltd.
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title_short	A fast multipole method for stellar dynamics
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