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Barnes-Hut Algorithm
CS498lvk
Abhinav S Bhatele
Feb 14th, ‘06
Introduction
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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)
Sequential Algorithm
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t=0
while t < t_final
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for i = 1 to n
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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
Forces on a particle
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Three major forces:
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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
Broad Overview
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Main Steps:
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Initialize the tree
In every iteration:
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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
Parallelization
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The step which we should parallelize to see
reasonable effects:
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Calculating forces on particles
For the sake of simplicity we might not
parallelize:
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Computing centroids and masses
Updating the particles
Migrating them
Any ideas/suggestions ??