TY - GEN
T1 - A cost optimal parallel algorithm for computing force field in N-body simulations
AU - Xue, Guoliang
PY - 1998/1/1
Y1 - 1998/1/1
N2 - We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n−1)/2 pairs, direct method requires Θ(n2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous Θ(n log n) time hierarchical tree algorithms were published by Appel [3] and by Barnes and Hut [4] respectively. In a recent paper, we presented a linear time algorithm which builds the oct tree bottom-up and showed that Appel’s algorithm can be implemented in Θ(n) sequential time. In this paper, we present an algorithm which computes the force field in Θ(log n) time using an processor CREWPR AM. A key to this optimal parallel algorithm is replacing a recursive top-down force calculation procedure of Appel by an equivalent non-recursive bottom-up procedure. Our parallel algorithm also yields a new Θ(n) time sequential algorithm for force field computation.
AB - We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n−1)/2 pairs, direct method requires Θ(n2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous Θ(n log n) time hierarchical tree algorithms were published by Appel [3] and by Barnes and Hut [4] respectively. In a recent paper, we presented a linear time algorithm which builds the oct tree bottom-up and showed that Appel’s algorithm can be implemented in Θ(n) sequential time. In this paper, we present an algorithm which computes the force field in Θ(log n) time using an processor CREWPR AM. A key to this optimal parallel algorithm is replacing a recursive top-down force calculation procedure of Appel by an equivalent non-recursive bottom-up procedure. Our parallel algorithm also yields a new Θ(n) time sequential algorithm for force field computation.
KW - Cost optimal algorithms
KW - Force field evaluation
KW - N-body simulations
KW - PRAM
KW - Paralle algorithms
KW - Spatial tree data structures
UR - http://www.scopus.com/inward/record.url?scp=0004914881&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0004914881&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0004914881
SN - 3540648240
SN - 9783540648246
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 95
EP - 104
BT - Computing and Combinatorics - 4th Annual International Conference COCOON 1998, Proceedings
A2 - Hsu, Wen-Lian
A2 - Kao, Ming-Yang
PB - Springer Verlag
T2 - 4th Annual International Computing and Combinatorics Conference, COCOON 1998
Y2 - 12 August 1998 through 14 August 1998
ER -