Broadband MLFMA with faster translations and optimal memory demand on the subwavelength levels

A broadband multilevel fast multipole algorithm (MLFMA) is presented based on the plane wave expansions for all translations on all division levels. For the out-to-in translation on the superwavelength levels we use the Rokhlin translator, and the exponential translator for the subwavelength levels. On those levels we also use a novel representation method for the far field and incoming wave patterns which enables as efficient saving of these field as with the multipole series technique but, in addition, allows the use of the diagonal translations and the FFT technique, which make all translations fast. The resulting broadband MLFMA has a complete error control up to 9 digits and is more efficient in both computational cost and memory demand than the traditional broadband MLFMA, which makes use of the multipole series on the subwavelength levels.