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I've been trying to understand the Fast Multipole Method but not really getting anywhere.

It seems like the fastest mainstream N-body simulation algorithm, and I would like to implement it in an efficient javascript version, mostly for amusement in browsers.

My math is pretty weak, but my programming is strong, relatively speaking. For example, I'm not even sure what "expansion" means mathematically in this context.

Can the implementation of FMM be described simply with words? Or is understanding of the math required?

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  • $\begingroup$ Your mileage may vary, but while I could imagine using an implementation of the Fast Multipole Method without understanding its mathematical justification, I would think a substantial understanding was needed to write and test an implementation. $\endgroup$ – hardmath Feb 1 '16 at 15:19
  • $\begingroup$ In terms of expansion: Expansion, or series expansion, is a method to approximate a function using a summation of a sequence of terms. The approximation gets better as more terms are added. See en.m.wikipedia.org/wiki/Taylor_series for more details. $\endgroup$ – Charles Feb 2 '16 at 5:11
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Actually I might have found a good explanation of the algorithm here: https://github.com/davidson16807/fast-multipole-method

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    $\begingroup$ Perhaps you could add a few more words about how this link leads to an answer of your Question? What does it really explain about the algorithm that you found useful, esp. as regards understanding or not understanding the math per your Question's context? If a link should go bad, knowing more about what was originally there can help to replace or recover it. Also it gives a Reader more of a basis to decide whether a link is worth following. $\endgroup$ – hardmath Feb 1 '16 at 15:22

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