Fast-integral-equation scheme for computing magnetostatic fields in nonlinear media

Computing magnetic field distributions is important for a range of practical applications. In the past, integral-equation-based schemes for such analysis have primarily relied on scalar formulations. In this paper, we introduce a novel integral equation that is cast in terms of the magnetic flux density and construct a method of moments solver by representing the flux with a set of basis functions whose normal component is continuous. This solver is then augmented with a recently introduced version of the fast multipole method that lowers the computational complexity and the memory requirements from 𝒪(N² ) to 𝒪(N), where N is the number of basis functions used for the analysis. We validate magnetic field distributions computed by the proposed scheme by comparing them with those obtained analytically. Finally, we demonstrate the efficacy of this scheme by applying it to the analysis of practical problems in the nonlinear regime