| In this thesis, an accelerated numerical procedure is introduced to iteratively evaluate the solution of the Lippmann-Schwinger integral equation modeling wave scattering by penetrable three-dimensional structures. The scheme allows for such evaluations in O(N log N) operations, where N is the number of the discretization points. A fast algorithm is introduced for the treatment of general scattering configurations: a specialized version is also presented to deal with bodies of revolution (BOR). The method achieves its efficiency through the use of the addition theorem. Fast Legendre Transforms (in the case of BOB) and Fast, Spherical Harmonics Transforms (in the general case). The convergence order of the method, on the other hand, is tied to the global regularity of the solution. At the lower end, it is second order accurate (third order in the far field) for discontinuous material properties. The order increases with increasing regularity leading to spectral convergence for globally smooth solutions. |
