Micromagnetic simulation by using the fast multipole method specialized for uniform brick elements

This paper describes a large-scale micromagnetic simulation by using the fast multipole method (FMM) specialized for uniform brick elements. The fast Fourier transform (FFT) is widely used to reduce computational costs of the demagnetizing field calculation. However, the FFT still requires operation counts of O (N log N), where N is the number of elements, which results in the huge computational costs in large-scale problems. To overcome the difficulties, we develop an O (N) approach based on the FMM. In a micromagnetic simulation, an analyzed region is usually subdivided into uniform elements. By making the best use of the periodic structure of uniformly distributed elements, the computational costs of the FMM can be reduced drastically. A large-scale micromagnetic simulation of a single-pole-type head demonstrates the effectiveness of the specialized FMM from the viewpoints of calculation time and memory requirements, compared with the FFT.