N-body simulation
• Available codes: http://nbody.sourceforge.net/
• MODEST: http://www.manybody.org/modest/
• Most often used for star cluster: AMUSE and
NBODY6/7
• Moving stars around:
http://www.artcompsci.org/kali/pub/msa/title.html
• Dark Energy Universe (DEUS) Simulation
http://www.deus-consortium.org/
• Complete overview: Sverre J. Aarseth, 2003,
Gravitational N-Body Simulations, Cambridge
University Press
What is a N-body simulation?
 Simulating the interaction of N objects in a
system
 No limitation of interpretation
 Examples:
– Movement of stars under the influence of gravity
in a galaxy
– Star cluster formation
– Clusters of galaxies
*Overview
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v2
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N-body problem
 Masses
 Locations
 Velocities
 Geometries
 Other Properties
Basic N-body Simulation
• Start with the N bodies
• Initial position and velocity
• For each time step acceleration of each body
is calculated, for example based on the
influence of gravity
• Velocity is updated based on acceleration
• Position is updated based on velocity
How to update the position and
velocity
• The simplest update step is a Forward Euler
algorithm:
• Not very accurate
• For the time step dt, a body is moving in
the vi direction
• Only correct at time i
Leap-Frog algorithm
• Position defined on integer time steps
• Velocity defined on integer + ½ time steps
• Velocity updated by (ai + ai+1) / 2
• The approximate value of a halfway between
time steps i and i + 1.
Parallel N-body methods
• Barnes-Hut algorithm (Barnes & Hut, 1986,
Nature, 324, 446)
• Fast Multipole Method
(http://www.ics.uci.edu/~ihler/papers/ihler_area.pdf)
• Parallel Multipole Tree algorithm