T - IfB

AP 3 M algorithmIf mass distribution is homogeneus then shortrange forces F s O(N) and long range forcesF l O(N lnN). But masses cluster under gravity(e.g. galaxies) and then F s O(N 2 ).One solution is to refine the mesh in the regionswhere the density of masses is denseusing the Adaptive P 3 M = AP 3 M algorithm.107Tree codesTreat clusters that are far away as quasi-particles.They form hierachical structures (clusters ofclusters). The bookkeeping of these structurescan be realized by trees (e.g. „quad-trees“). Treescan also be used in linked cell algorithms whenone has particles, i.e. cells, of very different size.„Many-Body Tree Methods in Physics“. by S. Pfalzner and P.Gibbon(Cambridge Univ. Press, N.Y., 2005)108