Fast steepest descent path algorithm for electromagnetic scattering problems in layered medium

The fast steepest descent path algorithm (FASDPA) is developed as a counterpart to the fast multipole method (FMM) for EM scattering problems. The basic idea of FASDPA is to expand the Green´s function as an integral summation of plane waves. Then the steepest descent path (SDP) is introduced to evaluate the integral efficiently. By separating the source and observation points into groups as has been done in FMM the acceleration of matrix-vector multiplication is possible. In observance of the integral representation of the Green´s function arising in a layered medium study, it is easy to see that the FASDPA can be applied to accelerate the computation.