Investigating the Fast Multipole Method (FMM)

For my numerical methods class, I studied the Fast Multipole Method (FMM). This clever technique allows for quick distance-independent calculations of far-field potential functions between many points. Envision a cluster of \(n\) stars interacting with each other gravitationally. To calculate the gravitational potential at each star from each other star, we would ordinarily need \(\mathcal{O}\left(n^2\right)\) operations, but with the FMM, this can be accelerated to a linear \(\mathcal{O}\left(n\right)\) operation.

If this sounds interesting, you can read my report as well as see the code I used to implement the method here.