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## An efficient program for many-body simulation (1985)

Venue: | SIAM J. Sci. and Stat. Comput |

Citations: | 166 - 0 self |

### Citations

2896 |
J.E.: The Design and Analysis of Computer Algorithms
- Ullman, Aho, et al.
- 1974
(Show Context)
Citation Context ...putation were made faster. The initial step was the use of a new algorithm with lower asymptotic time complexity; the use of a better algorithm is often the way to achieve the greatest gains in speed =-=[2]-=-. Since every particle attracts each of the others by the force of gravity, there are O(N2) interactions to compute for every iteration. Furthermore, for the same reasons that the closed form integral... |

1524 |
Multidimensional binary search trees used for associative searching
- Bentley
- 1975
(Show Context)
Citation Context ... clumps consist of one galaxy each. Note that this procedure does not require that the number of clumps be a power of two, although that might seem most natural. This structure is known as a k-d tree =-=[4]-=-. It has a variety of applications in multidimensional problems, including searching, nearest-neighbor calculations, classification, numerical integration, and computing minimum spanning trees [10], [... |

764 | An algorithm for finding best matches in logarithmic expected time.
- Friedman, Bentley, et al.
- 1977
(Show Context)
Citation Context ...ree [4]. It has a variety of applications in multidimensional problems, including searching, nearest-neighbor calculations, classification, numerical integration, and computing minimum spanning trees =-=[10]-=-, [5], [11]. For a many-body application, a standard k-d tree will be far from optimalmnearby objects will not be in the same clump much of the time. The Grab procedure, though its behavior is difficu... |

694 |
Computer Simulation Using Particles
- Hockney, Eastwood
- 1988
(Show Context)
Citation Context ...t clusters of three or more particles. Another similar approach is to divide the universe into cells, computing the particle-particle interactions within the cell, and then the cell-cell interactions =-=[13]-=-. This has complexity O(N4/3) for a uniform distribution. A variant of this method is to compute the cell-cell interactions by a fast Fourier transform, reducing the complexity to O(N log N)). Both va... |

18 |
A parallel algorithm for constructing minimum spanning trees
- Bentley
- 1980
(Show Context)
Citation Context ...]. It has a variety of applications in multidimensional problems, including searching, nearest-neighbor calculations, classification, numerical integration, and computing minimum spanning trees [10], =-=[5]-=-, [11]. For a many-body application, a standard k-d tree will be far from optimalmnearby objects will not be in the same clump much of the time. The Grab procedure, though its behavior is difficult to... |

14 | Classical Mechanics - Desloge - 1982 |

11 | A nested partitioning procedure for numerical multiple integration,ā
- Friedman, Wright
- 1981
(Show Context)
Citation Context ... has a variety of applications in multidimensional problems, including searching, nearest-neighbor calculations, classification, numerical integration, and computing minimum spanning trees [10], [5], =-=[11]-=-. For a many-body application, a standard k-d tree will be far from optimalmnearby objects will not be in the same clump much of the time. The Grab procedure, though its behavior is difficult to analy... |

8 |
The theory of the large scale structure of the universe. The large scale structure of the universe
- Zeldovich
(Show Context)
Citation Context ... in a radiation-dominated universe). Two of the competing theories describing the formation of galaxies [21] may be characterized as "top-down" and "bottom-up," respectively. In the "top-down" theory =-=[22]-=-, galaxy clusters formed as a result of long-range pressure waves left over from the radiation-dominated universe. A pressure wave contains alternating regions of high and low density. When the univer... |

6 |
Stellar Dynamics in a Discrete Phase Space
- Miller, Prendergast, et al.
- 1968
(Show Context)
Citation Context ...y problem. One approach is to represent the problem in a position-velocity phase space, and transform the force field using a fast Fourier transform into a form where it can be applied in linear time =-=[15, 16]-=-. This takes O(NlogN) time (dominated by the Fourier transform) per iteration. However, the phase space must be discrete. This means that all positions must be multiples of some lattice size a, and th... |

5 |
Numerical experiments on spiral structure
- Miller, Prendergast, et al.
(Show Context)
Citation Context ...y problem. One approach is to represent the problem in a position-velocity phase space, and transform the force field using a fast Fourier transform into a form where it can be applied in linear time =-=[15, 16]-=-. This takes O(NlogN) time (dominated by the Fourier transform) per iteration. However, the phase space must be discrete. This means that all positions must be multiples of some lattice size a, and th... |

1 |
An investigation ofgalaxy clustering using an asymptoticallyfastN-body algorithm, Undergraduate Thesis
- APPEL
- 1981
(Show Context)
Citation Context ...red to calculate the acceleration between two bodies can be estimated at 100 clock cycles (40 of which are needed for a calculation of a periodic distance function peculiar to the many-galaxy problem =-=[3]-=-). The time for one clock cycle is 12 nanoseconds [19], and the number of pairs of bodies is N2/2, so the time for one iteration can be estimated at .6N2 microseconds. Using scalar instructions, or us... |

1 |
Numerical treatment of ordinary differettial equations by extrapolation methods
- BULIRSCH, STOER
- 1966
(Show Context)
Citation Context ...e minimum characteristic time dt is found. The procedure Move calculates the new velocities and positions: Vne Vold if- A. dt, Pnew Pond + Vnew" dr. There are schemes such as Richardson extrapolation =-=[6]-=- which improve on this "naive" method of integration and allow the use of a larger timestep with great accuracy. However, the timestep will still be no larger than that allowed by setting to 2 in the ... |

1 |
The big bang cosmologymenigmas and nostrums
- DICKE, PEEBLES
- 1979
(Show Context)
Citation Context ...viation of p from Pcrit in the early universe (t 1 sec) would be enormously amplified as the universe expanded, making the current measured value of/9 0.1pcri far too close to have happened by chance =-=[8]-=-. The astronomical search for the "missing mass"--to determine whether P/Pcrit is closer to 0.1 or to 1.0mis complicated by the fact that many forms of mass (such as black holes) are difficult to obse... |

1 |
Dvumernaya model obrazovaniya krupnomasshtabnoi struktury vselennoi (A two-dimensional model of the formation of large-scale structures
- SIGOV, SHANDARIN
- 1978
(Show Context)
Citation Context ...es; that galaxies formed within these super-clusters; and that stars formed within the galaxies. Two-dimensional simulations under these assumptions have shown a cell-like structuring of the clusters =-=[9]-=-; it is not clear whether the dimensionality of the simulation is responsible. It may be that these cells exist in the present universe [14], but the observations at large distances are not conclusive... |

1 |
Yacheiskaya struktura vselennoi (The cell structure of the universe
- JOEVEER, EINASTO, et al.
- 1977
(Show Context)
Citation Context ...sumptions have shown a cell-like structuring of the clusters [9]; it is not clear whether the dimensionality of the simulation is responsible. It may be that these cells exist in the present universe =-=[14]-=-, but the observations at large distances are not conclusive. In the "bottom-up" theory [17], there were no pressure waves, and the universe immediately after condensation consisted of randomly distri... |

1 |
The CRAY-1 computer system, in Computer Structures: Principles and Examples
- RUSSELL
- 1982
(Show Context)
Citation Context ...can be estimated at 100 clock cycles (40 of which are needed for a calculation of a periodic distance function peculiar to the many-galaxy problem [3]). The time for one clock cycle is 12 nanoseconds =-=[19]-=-, and the number of pairs of bodies is N2/2, so the time for one iteration can be estimated at .6N2 microseconds. Using scalar instructions, or using vector instructions with inefficient pipeline beha... |