Fast Multipole Method Applied to Volume Integral Equation Method

Abstract. The Volume Integral Equation Method (VIEM) has been used for the solution of three-dimensional non-linear magnetostatic field problems. The number of unknowns is minimal as only the magnetic material has to be discretized. For accurate solutions of problems where the magnetic field is small compared to the excitation field a difference field formulation has been developed. To reduce computational costs the fast multipole method is applied both on compression of the system matrix and during post processing. The efficiency of the formulation is demonstrated in several examples.