A Hybrid Broadband Fast Multipole Algorithm

A broadband fast multipole algorithm (FMA) is proposed using a hybridization of the plane wave and multipole expansions of the Green's function. By representing the low order harmonics using the plane wave expansion and representing the high order harmonics using the multipole expansion, the proposed method is accurate at all frequencies. The error analysis is performed to achieve arbitrarily high accuracies. The method can be regarded as a unification of the conventional dense and diagonal FMAs. Numerical examples are presented to demonstrate the accuracy of the method.