Published online by Cambridge University Press: 18 August 2009
Introduction
Direct N-body simulations are of necessity expensive because of the need to evaluate all the N(N –1)/2 force interaction terms. We have seen that the Ahmad–Cohen [1973] neighbour scheme only alleviates the problem to some extent. However, once the particle number becomes sufficiently large, the dynamical behaviour begins to change because close encounters are less important. This behaviour has inspired methods for collisionless systems to be developed, such as tree codes or multipole expansions. In this chapter, we are concerned with tree codes since some relevant aspects of the latter have already been discussed. First we review the basic features of the pioneering Barnes & Hut [1986] scheme which is widely used in a variety of applications. Since the emphasis in this book is on collisional stellar dynamics, we devote a section to describing a tree code for point-mass interactions [McMillan & Aarseth, 1993] in the hope that it might be revived. The final section deals with an independent development for flattened systems [Richardson, 1993a,b] that has been used to study different stages of planetary formation as well as ring dynamics, where collisions play an important role.
Basic formulation
In view of the rapid growth in the computational requirements for increasing particle numbers when using direct summation, it is not surprising that several tree-based approaches have been made to speed up the expensive force calculation.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.