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 -