Precorrected-FFT algorithm for solving combined field integral equations in electromagnetic scattering

Abstract

The precorrected-FFT method is applied in this paper to solve the combined field integral equation (CFIE) for scattering by arbitrarily shaped three-dimensional conductors. The object is first discretized using triangular elements with the Rao-Wilton-Glisson (RWG) basis functions. The source singularities on the original triangular meshes are then projected onto uniform rectangular grids, which enables the calculation of the resultant matrix-vector product to be performed by using the fast Fourier transforms. The memory requirement and computational complexity of the resulting algorithm are of O(N1.5) and O(N1.5 log N), respectively, where N denotes the number of unknowns. In addition, the employment of CFIE eliminates the interior resonance problem suffered by both the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) and thus significantly improves the convergence of the iterative solution. A unique advantage of the present method is that the computational expense per iteration of CFIE is almost the same as that of EFIE. This fast algorithm renders problems associated with electromagnetic scattering by large complex objects be handled on a normal personal computer.