Download:
|
by R Fl, Feng Zhao, S. Lennart Johnsson
Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175, USA
http://www.parc.xerox.com/spl/members/zhao/papers/pmm.ps
Add To MetaCart
Abstract:
This paper reports on a fast implementation of the three-dimensional nonadaptive Parallel Multipole Method (PMM) on the Connection Machine system model CM--2. The data interactions within the decomposition tree are modeled by a hierarchy of three dimensional grids forming a pyramid in which parent nodes have degree eight. The base of the pyramid is embedded in the Connection Machine as a three dimensional grid. The standard grid embedding feature is used. For 10 or more particles per processor the communication time is insignificant. The evaluation of the potential field for a system with 128k particles takes 5 seconds, and a million particle system about 3 minutes. The maximum number of particles that can be represented in 2G bytes of primary storage is 50 million. The execution rate of this implementation of the PMM is at about 1.7 Gflops/sec for a particle-processor-ratio of 10 or greater. A further speed improvement is possible by an improved use of the memory hierarchy associated with each floating-point unit in the system.
Citations
|
398
|
A fast algorithm for particle simulations
– Greengard, Rokhlin
- 1987
|
|
88
|
A fast adaptive multipole algorithm for particle simulations
– Carrier, Greengard, et al.
- 1988
|
|
78
|
Communication efficient basic linear algebra computations on hypercube system
– Johnsson
- 1987
|
|
50
|
A parallel version of the fast multipole method
– Greengard, Gropp
- 1990
|
|
41
|
An O(N) Algorithm for Three-Dimensional N-Body Simulations, AI-TR-995
– Zhao
- 1987
|
|
41
|
The parallel multipole method on the connection machine
– Zhao, Johnsson
- 1991
|
|
29
|
Embedding of Grids into Optimal Hypercubes
– Chan
- 1991
|
|
24
|
Embedding meshes in Boolean cubes by graph decomposition
– Ho, Johnsson
- 1990
|
|
19
|
B-valuation of graphs
– Havel, Mov'arek
|
|
19
|
Optimizing tridiagonal solvers for alternating direction methods on Boolean cube multiprocessors
– HO, JOHNSSON
- 1990
|
|
15
|
Dilation-2 embeddings of grids into hypercubes
– Chan
- 1988
|
|
11
|
and Piet Hut. A hierarchical o(n log n) force calculation algorithm
– Barnes
- 1986
|
|
6
|
The Rapid Evaluation of Potential Fileds in Particle Systems
– Greengard
- 1988
|
|
6
|
On the efficient implementation of the fast multipole method
– Greengard, Rokhlin
- 1988
|
|
6
|
On the embedding of arbitrary meshes in boolean cubes with expansion two dilation two
– Ho, Johnsson
- 1987
|
|
5
|
Odd-even Cyclic Reduction on Ensemble Architecture and the Solution of Tridiagonal System of Equations
– Johnsson
- 1984
|
|
3
|
Optimal Communication in Distributed and Shared Memory Models of Computation on Network Architectures
– Johnsson
- 1990
|
|
3
|
Multiple tridiagonal systems, the alternating direction method, and Boolean cube configured multiprocessors
– Johnsson, Ho
- 1987
|
|
2
|
Embeddings of 3-dimensional grids into optimal hypercubes
– Chan
- 1990
|
|
2
|
Johnsson and Peggy Li. Solutionset for AMA/CS 146
– Lennart
- 1983
|
|
1
|
Computational structure of the n-body problem
– Katsenelson
- 1989
|
