A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.