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Derivator

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barnes hut method approximates the interaction by treating a bunch of far away particles as one big particle located in the center of mass of the bunch of particles.

My lecture notes say, that the fast multipole methode not only does the above 'barnes hut' approximation, but also assumes, that the potential varies only slowly in the region where the particle for which the interactions should be computed is located.

In the fast multipole method, there is a multipole expansion and a taylor expansion. Is the taylor expansion modelling the slow variation of the potential, or is the taylor expansion responsible for the fact that far away bunches of particles are treated as one big single particle? Or is this for what the multipole expnsion is responsible for?

Could somone please explain?

best,

derivator