Broadband MLFMA with plane wave expansions and optimal memory demand

A broadband multilevel fast multipole algorithm (MLFMA) in 3D is presented based on plane wave expansions and diagonal translations on all division levels. The radiation and incoming wave patterns on all levels are presented by trigonometric polynomials, and optimal sampling rates and translator degrees are found and tabulated. On the super-wavelength levels the memory need and the computational cost are lowered more than by half compared to the traditional approach. On the sub-wavelength levels also a novel saving method for the field patterns is presented which is as efficient as saving the multipole series coefficients while all translations with the proposed method can still be carried out in the fast diagonal form. Also the direction dependence of the radiation and incoming wave patterns is lowered by half. The proposed broadband MLFMA has a very good error control on all division levels which we demonstrate by numerical testing.