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

A number of techniques have been proposed to speed up the evaluation of matrix-vector multiplication in method of moments iterative solvers. One of these, the adaptive integral method (AIM) projects triangular elements onto uniform grids with the aid of auxiliary basis functions and then carries out the matrix-vector multiplication by the fast Fourier transforms (FFT). We present the precorrected-FFT method, originally proposed to solve electrostatic problems (see Phillips, J.R. and White, J.K., 1997). In an earlier extension by the authors to solve 3D scattering problems in free space, the precorrected-FFT formulations for only the EFIE were presented. A combination of the EFIE and MFIE, namely the combined field integral equation (CFIE), has been found to be able to eliminate the interior resonance problem suffered by both EFIE and MFIE and to converge much faster (see Wang, C.F. et al., 1998). The present method can achieve good results of the same accuracy as AIM, but with a grid spacing at least two to three times larger. The algorithm is implemented in a way that requires no extra computational expense as compared with those in EFIE, which leads to another advantage over the AIM based method.