Fast Multipole Method (FMM) is a mathematical technique which was developed to seek rapid solutions to integral equations of scattering for Helmholtz problems. For scattering problems, the integral equation is discretized into a matrix equation by the method of moments (MoM). The resultant equation is then typically solved by the direct LU, or an iterative method which requires O(N3) or O(N2) floating point operations respectively. However, if FMM is implemented, the complexity is reduced to O(N3/2). Moreover, the multilevel fast multipole algorithm (MLFMA) which is a multistage FMM can further reduce the complexity to O(NlogN). These methods are promising for providing a path to large scale computing in electromagnetics.
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