Computational Structure of the N-Body Problem

Katzenelson, Jacob

doi:10.1137/0910048

Cited by 50 publications

(20 citation statements)

References 6 publications

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“…In this article, we are restricted to an equispaced DFT but we use a different set of interpolating functions that offer greater accuracy in this restricted case. We also compute it in parallel, using the method of Greengard and Gropp [10] and Katzenelson [11].…”

Section: Algorithm 2: Fast Multipole Approachmentioning

confidence: 99%

The Future Fast Fourier Transform?

Edelman¹,

McCorquodale²,

Toledo³

1998

SIAM J. Sci. Comput.

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It seems likely that improvements in arithmetic speed will continue to outpace advances in communications bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does not have sufficient storage capacity. For these reasons, we propose that an inexact DFT such as an approximate matrixvector approach based on singular values or a variation of the Dutt-Rokhlin fastmultipole-based algorithm [9] may outperform any exact parallel FFT. The speedup may be as large as a factor of three in situations where FFT run time is dominated by communication. For the multipole idea we further propose that a method of "virtual charges" may improve accuracy, and we provide an analysis of the singular values that are needed for the approximate matrix-vector approaches.

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Section: Algorithm 2: Fast Multipole Approachmentioning

confidence: 99%

The Future Fast Fourier Transform?

Edelman¹,

McCorquodale²,

Toledo³

1998

SIAM J. Sci. Comput.

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“…The Barnes-Hut (BH) algorithm [3] is one of a number of algorithm [2,3,6,7,9] that uses a multiple expansion and a hierarchical data structure to reduce the complexity of computing long-range interactions like gravity. The multipole expansion allows one to treat a collection of bodies as a point mass (perhaps with quadrupole and higher moments) located at the center of mass.…”

Section: N-body Problem and The Barnes-hut Methodsmentioning

confidence: 99%

“…The example problem we use in this paper is a simulation of interacting galaxies from astrophysics. The problem studies how the positions and velocities of stars in the galaxies evolve with time under the gravitational forces that the stars exert on one another [2,4,6,7,9] . This application was ported to an Intel Paragon and Cray T3D and measurements were collected to study overhead and scalability.…”

Section: Application and System Scopementioning

confidence: 99%

Evaluating Budget of Overhead and Scalability on High-Performance Computing Systems

Almojel¹

2005

sci

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ABSTRACT. High-Performance Computing Systems (HPCS) based on parallel processing have the potential for satisfying the rapid growth in computational requirements at economical costs. As such machines grow in size, however, parallelization overhead grows in a manner that can limit scalability. This work sheds some light on the sources, dynamics, and magnitudes of the different types of overhead and their impact on performance. Results are obtained through experimental measurements of one of the NASA Earth and Space Sciences (ESS) applications running on the Jet Propulsion Laborator y/Earth and Space Sciences High-Performance Computing (HPC) systems.

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“…zo is fixed in the mean position of the foil, and an observer in this reference frame will see the foil oscillating in heave and pitch and a free stream Uo flowing from left to 38 right. The motion of the foil has the following form:…”

Section: Coordinate Systemsmentioning

confidence: 99%

Extracting energy from unsteady flows through vortex control

Streitlien¹

1994

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Computational Structure of the N-Body Problem

Cited by 50 publications

References 6 publications

The Future Fast Fourier Transform?

The Future Fast Fourier Transform?

Evaluating Budget of Overhead and Scalability on High-Performance Computing Systems

Extracting energy from unsteady flows through vortex control

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