I'm interested in implementing the Fast Multipole Method to efficiently simulate a system of repulsive particles.
I've found a large collection of references discussing FMM, but none seem very approachable for non-mathematicians who want to fully understand the algorithm.
Can you recommend a ground-up reference that clearly explains the mathematics behind the process, and includes pseudocode exemplifying a proper implementation?
I am by no means an expert in FMM, but this java implementation and introduction is the best source I've found so far for explaining it carefully and slowly. The paper is good at defining terms before using them, and the code at least is useful as a reference point. The math still gets hairy very quickly, but it is what it is :)
A pedestrian introduction to fast multipole methods is a close second. It doesn't explain the actual details of a working FMM implementation, but it's a good introduction to the basic ideas.