This site has been set up to provide literature, software and related information on hierarchical tree methods - techniques for performing rapid summation of potentials and forces for electrostatic or gravitational N-body systems.

(This page is a replacement for the former

Many Body Tree Methods in Physics

book cover

by Susanne Pfalzner and Paul Gibbon

An introductory 'How-To' for hierarchical tree methods, describing the principles of rapid force-summation for N-body systems governed by long-range interaction potentials. This type of N2 problem crops up in many areas of physical sciences, such as astrophysics, plasma physics, condensed matter physics and materials science.


  1. Introduction
  2. Basic structure of the hierarchical tree method
  3. Open boundary problems
  4. Optimization of hierarchical tree codes
  5. Periodic boundary conditions
  6. Periodic boundary problems
  7. The fast multipole method
  8. Appendices

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tarball Description Language
Book Chapters
harc3d.tar.gz Simple electrostatic code for 2 charge species f77 Compiles but probably won't run any more without some serious debugging. Closely adheres to original recursive Barnes-Hut algorithm. 2
beamtree.tar.gz Particle beam propagation f77 Includes routines for speed/accuracy benchmarking 2,3
treemd.tar.gz 'Barnes-Hut-Ewald' code for dense plasma studies f77 Includes fully periodic boundary conditions using tabulated Ewald sums. Used previously for inverse bremsstrahlung studies (see: Pfalzner & Gibbon, Phys. Rev. E 1998). 4,5,6
clustree.tar.gz Open boundary electrostatic code for clusters (Coulomb explosions) f77 Stripped down version of treemd. Uses vectorised 'level-by-level' tree building and traversals. 4, 6
PEPC Link to the PEPC project: parallel multi-purpose tree code f90 Separated tree kernel and physics components allowing easy adaptation to new applications.  
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