On the order and complexity of higher order MLFMA for 3D electromagnetic scattering

Based on the multilevel fast multipole algorithm (MLFMA), higher order MLFMA is an efficient method for 3D EM scattering nowadays, especially for large electrical targets. However, the application of this method is limited by the compatibility between the higher order method and MLFMA. For a given object, higher order MLFMA has different properties when the order and the finest cube size of MLFMA is changed. The computational complexity, including the memory requirement and main computational time under different conditions, such as different orders, different number of levels, different finest cube size, in the case of conducting sphere scattering, were investigated in detail In this work. Numerical results show the relation.