To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Barnes–Hut simulation

From Wikipedia, the free encyclopedia

A 100-body simulation with the Barnes–Hut tree visually  as blue boxes.
A 100-body simulation with the Barnes–Hut tree visually as blue boxes.

The Barnes–Hut simulation (named after Josh Barnes and Piet Hut) is an approximation algorithm for performing an n-body simulation. It is notable for having order O(n log n) compared to a direct-sum algorithm which would be O(n2).[1]

The simulation volume is usually divided up into cubic cells via an octree (in a three-dimensional space), so that only particles from nearby cells need to be treated individually, and particles in distant cells can be treated as a single large particle centered at the cell's center of mass (or as a low-order multipole expansion). This can dramatically reduce the number of particle pair interactions that must be computed.

Some of the most demanding high-performance computing projects do computational astrophysics using the Barnes–Hut treecode algorithm, such as DEGIMA.[2][citation needed]


The Barnes–Hut tree

In a three-dimensional n-body simulation, the Barnes–Hut algorithm recursively divides the n bodies into groups by storing them in an octree (or a quad-tree in a 2D simulation). Each node in this tree represents a region of the three-dimensional space. The topmost node represents the whole space, and its eight children represent the eight octants of the space. The space is recursively subdivided into octants until each subdivision contains 0 or 1 bodies (some regions do not have bodies in all of their octants). There are two types of nodes in the octree: internal and external nodes. An external node has no children and is either empty or represents a single body. Each internal node represents the group of bodies beneath it, and stores the center of mass and the total mass of all its children bodies.

Calculating the force acting on a body

To calculate the net force on a particular body, the nodes of the tree are traversed, starting from the root. If the center of mass of an internal node is sufficiently far from the body, the bodies contained in that part of the tree are treated as a single particle whose position and mass is respectively the center of mass and total mass of the internal node. If the internal node is sufficiently close to the body, the process is repeated for each of its children.

Whether a node is or isn't sufficiently far away from a body, depends on the quotient , where s is the width of the region represented by the internal node, and d is the distance between the body and the node's center of mass. The node is sufficiently far away when this ratio is smaller than a threshold value θ. The parameter θ determines the accuracy of the simulation; larger values of θ increase the speed of the simulation but decreases its accuracy. If θ = 0, no internal node is treated as a single body and the algorithm degenerates to a direct-sum algorithm.

See also

References and sources

  1. ^ Gibbon, Susanne Pfalzner ; Paul (1996). Many-body tree methods in physics. Cambridge [u.a.]: Cambridge Univ. Press. pp. 2, 3. ISBN 978-0-521-49564-6.
  2. ^ Hamada T. et al. (2009) A novel multiple-walk parallel algorithm for the Barnes–Hut treecode on GPUs – towards cost effective, high performance n-body simulation. Comput. Sci. Res. Development 24:21–31. doi:10.1007/s00450-009-0089-1

External links

This page was last edited on 14 July 2019, at 16:11
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.