On Jan 28, 2009, at 5:00, Eric Lavigne wrote:

> In "Objective CAML for Scientists" [1] pages 92-101 Jon Harrop  
> demonstrates a rapid numerical solution for a multibody gravitation  
> problem, which looks similar to the problem you are solving. He  
> refers to the method as Fast Multipole Method [2,3]. It trades a  
> little accuracy for a big performance gain. Oh, and his  
> implementation in OCaml

The Fast Multipole Method is an algorithm for rapidly calculating all  
pairwise interactions between a set of objects, provided that the  
interactions have a particular form. The method was developed for  
gravitational interactions (e.g. between planets or stars) and for  
electrostatic interactions (e.g. between atoms), which are two types  
of interactions that have the same mathematical form: the energy is  
inversely proportional to the distance between two objects.

It is possibe to generalize the Fast Multipole Method somewhat, but  
it remains a technique for a limited (though important) class of  
interactions. It is rather unlikely that it will be of any use for  
simulating a flock of birds.

Konrad.



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