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

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