Fast Directional Multilevel Algorithm for Analyzing Wave Scattering

A new method named fast directional multilevel algorithm is proposed for analyzing wave scattering. Similar to a fast multipole method, an oct-tree structure is used in the new method. Unlike the conventional MLFMA, the kernel is evaluated by a new method, instead of approximating the Green's function by multipole expansion. The fast directional multilevel algorithm is first used to solve the wave scattering problem via combined field integral equation (CFIE) using Rao-Wilton-Glisson (RWG) basis functions. The low rank representations are extended to apply in the low frequency regime which is proved efficient and stable. The numerical results demonstrate that the computational complexity of this new multilevel algorithm can achieve the complexity of O(N log N). This algorithm is robust and performs well on other oscillatory kernels because of its not depending on the explicit form of kernels.