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Suppose I have $n$ electric point charges in, say, two dimensions. Is there any algorithm (and I have a hunch that it might be related to the Fourier transform) to compute the net forces that act on each point charge in less than $O(n^2)$, preferably something like $O(n \log n)$? Thanks!

An approximation might be good enough for my use case.

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The FFT is an important part of the fast multipole method, which is probably what you would want to use.

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