The fast steepest descent path algorithm (FASDPA) for analyzing scattering from two-dimensional scatterers

The electromagnetics community has shown a renewed interest in iterative solvers as a means for solving very large scattering problems. A number of techniques have been proposed that permit fast matrix-vector multiplications of matrices that arise in the method of moments (MoM). Multilevel versions of the fast multipole method (FMM), the multilevel fast multipole algorithm (MLFMA), and the multilevel matrix decomposition algorithm (MLMDA) have been developed. The cost per iteration of these algorithms scales as O(NlogN) and O(Nlog/sup 2/N), respectively. Although multilevel algorithms asymptotically exhibit the lowest possible computational cost, they are typically outperformed by two-level algorithms for problems involving moderate size scatterers. The computational complexity of the proposed FASDPA is O(N/sup 4/3/) per iteration without proceeding to a multi-level scheme.