An enhanced mixed-form fast multipole algorithm using rotation methods

In this paper, the broadband accuracy of the mixed-form fast multipole algorithm (MF-FMA) is improved by applying rotation techniques. Two kinds of rotation methods are employed respectively. One is the coordinate system rotation technique. The other one is the pseudospectral projection based on fast Fourier transform (FFT). Either of them has certain advantages depending on the number of multipoles. Through rotation, translation matrices become very sparse, which enables us to save the storage as well as the CPU time. Hence, we can increase the number of multipoles in the low frequency regime to shift up the transition region of MF-FMA. The overall accuracy is thereby improved significantly.