Simulation of Arbitrarily-shaped Magnetic Objects

We propose a novel method for simulating rigid magnets in a stable way. It is based on analytic solutions of the magnetic vector potential and flux density, which make the magnetic forces and torques calculated using them seldom diverge. Therefore, our magnet simulations remain stable even though magnets are in close proximity or penetrate each other. Thanks to the stability, our method can simulate magnets of any shapes. Another strength of our method is that the time complexities for computing the magnetic forces and torques are significantly reduced, compared to the previous methods. Our method is easily integrated with classic rigid-body simulators. The experiment results presented in this paper prove the stability and efficiency of our method.