An improved fast steepest descent path algorithm

We have presented a modification of the fast steepest descent gradient path algorithm (FASDPA) for 2-D scattering. The computational cost of the FASDPA is lower than that of the previously developed fast multipole method (FMM) and ray propagation fast multipole algorithm (RPFMA), both for two-level and multi-level implementations. The method, which uses an interpolated far field pattern to arrive at an efficient representation of the integral along the steepest descent path, has inherent advantages such as simplicity and ease of diagonalization.