Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization

A fast recursive algorithm has been developed to solve for the scattering solution of a large 2‐D inhomogeneous body for TM waves. The inhomogeneous body is first divided into N subscatterers. The algorithm uses an aggregate T̄ matrix and translation formulas to solve for the solution of n + 1 subscatterers from the solution for n subscatterers. The computational complexity of the algorithm is of O(NMP2), where NM is the number of unknowns and P is the number of harmonies required in the translation formulas. The memory requirement is proportional to the number of unknowns. The algorithm has been used to solve for the scattering solution of a 10‐λ‐diameter two‐dimensional scatterer with about 12,000 unknowns, taking about 30 s on a CRAY‐2 supercomputer.