Skeletons from the treecode closet (Q1326723)

We consider treecodes (\(N\)-body programs which use a tree data structure) from the standpoint of their worst-case behavior. That is, we derive upper bounds on the largest possible errors that are introduced into a calculation by use of various multipole acceptability criteria (MAC). We find that the conventional Barnes-Hut MAC can introduce potentially unbounded errors unless \(\theta<1/\sqrt 3\), and that this behavior while rare, is demonstrable in astrophysically reasonable examples. We consider two other MACs closely related to the Barnes-Hut MAC.