This paper describes the implementation of the fast Fourier transform on multipole (FFTM) algorithm for rapid calculation of magnetostatic fields in micromagnetics. The method is based on the multipole approximation theory, in which the computation-intensive transformation operations of the multipole in local expansions are accelerated by using FFT algorithms. Hence, this algorithm has the computational efficiency of the FFT-based approach, but is not confined to use in problems with regularly spaced elements.Index Terms-Fast Fourier transform on multipole (FFTM), magnetostatic fields, micromagnetic simulations, multipole approximations.

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