On the complexity and accuracy of MLFMA for 3D electromagnetic scattering

As the fastest numerical solver for 3D electromagnetic scattering up to now, multilevel fast multipole algorithm (MLFMA) has the excellent property. The computational complexity and the storage requirement is O(NlogN) and O(N) respectively, for a N unknowns problem. For a given object, MLFMA has different property and accuracy when the discretization density and the grouping technique of MLFMA change. This paper investigates the computational complexity, the storage requirement and the accuracy of MLFMA in case of conducting sphere scattering in details. It is shown a good property including the complexity and accuracy can be achieved when a suitable discretization density and the grouping size are chosen.