Fast multipole acceleration using impedance matrix localization

In the past, a variety of computational schemes has been developed for analyzing electromagnetic scattering from two dimensional (2D) objects. The impedance matrix localization method (IML) developed by Canning [199] constitutes a different method for speeding up MOM matrix-vector multiplications. The IML is designed for objects that are smooth on the scale of the wavelength, and relies on a transformation that numerically sparsifies the MOM matrix. This is achieved by using basis functions that radiate strongly in preferred directions. In this paper, a hybrid IML-FMM (fast multipole method) technique is presented. The IML is used to sparsify the FMM far-field transformation matrices to further speed up the MOM matrix-vector multiplication. Although the proposed method does not decrease the rate of scaling of the computational cost, it does significantly reduce the actual cost associated with the solution of many practical 2D scattering problems. Furthermore, a windowed translation operator is also used, yielding an efficient O(N/sup 4/3/) FMM code for analyzing scattering from 2D perfect electrically conducting surfaces.