I am trying to optimize an engineering setup which involves an arrangement of permanent neodymium magnets in 3d space. I am planning on using Houdini to solve the optimization as a simulation, which I can handle all of the coding and setup for doing that. What I need is a method to actually calculate the interactions between N magnets in 3 space. I have been searching for a few months and haven't found any really solid information which I can penetrate.
My Background: I have a BS in Applied Mathematics and have been coding for about 10 years now. Not a newbie at this, but PDE was not one of my strong subjects and I feel like that is where my conceptual failure is.
The project is essentially an attempt at a self centering magnetic bearing built almost entirely of permanent magnets. I have a hypothetical structure for passive corrections to the centering, but I need to optimize the balance before I can really get into that as I need to know just how unstable the minimized variance will be and under what conditions. Computing time isn't an issue as I have a few thousand hours on a simulation farm to utilize.