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.

  • $\begingroup$ Do you just need the interactions between the permanent magnets, or are there significantly paramagnetic or ferromagnetic entities in the picture? By interactions do you mean the force and torque on each magnet? Do you get to choose the shapes of your magnets (the problem would be trivial if you could use spherical magnets)? $\endgroup$ – user5713492 Oct 11 '18 at 2:24

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