Translation Procedures for Broadband Mlfma

The multilevel fast multipole algorithm (MLFMA) is used in computing acoustic and electromagnetic fields with integral equation methods. The traditional MLFMA, however, suffers from a lowfrequency breakdown that effectively limits the minimum division cube side length to approximately one wavelength. To overcome this low-frequency breakdown and get a broadband MLFMA, we propose an efficient and relatively straightforward implementation of the field translations based on the spectral representation of the Green’s function. As an alternative we also consider the so called uniform MLFMA, which has a lower computational cost but limited accuracy. We consider the essential implementation details and finally provide numerical examples to demonstrate the error controllability of the translations.