Barnes-Hut Algorithm CS498lvk

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Barnes-Hut AlgorithmCS498lvk

• Abhinav S Bhatele
• Feb 14th, 06

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Introduction

• The algorithm was presented in "A Hierarchical
  O(n log n) force calculation algorithm" by J.
  Barnes and P. Hut in Nature, v. 324, December
  1986
• It is a solution to the N-body problem and is
  widely used in astrophysics
• It has been thoroughly parallelized
• However it is not accurate as some other methods
  like the Fast Multipole Method (FMM)

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Sequential Algorithm

• t 0
• while t lt t_final
• for i 1 to n
• compute f(i) force on particle i
• move particle i under force f(i) for time dt
• end for
• compute interesting properties of particles
• t t dt
• end while

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Forces on a particle

• Three major forces
• External force
• Nearest Neighbour forces
• Far Field Forces these are the ones difficult
  to parallelize
• The third force calculation takes 0(n2) which
  is reduced to 0(n log n) by use of divide and
  conquer algorithms
• To reduce the no. of particles in the force
  calculation, we use quad-trees and oct-trees
• Make use of adaptive quad-trees when distribution
  of particles bounded in the box is uneven

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Broad Overview

• Main Steps
• Initialize the tree
• In every iteration
• Compute the center of mass and total mass of each
  subtree
• Compute the forces on each particle
• Update the positions according to the forces
• Migrate the particles

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Parallelization

• The step which we should parallelize to see
  reasonable effects
• Calculating forces on particles
• For the sake of simplicity we might not
  parallelize
• Computing centroids and masses
• Updating the particles
• Migrating them

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Any ideas/suggestions ??