The efficient implementation of IE-FFT algorithm with combined field integral equation for solving electromagnetic scattering problems

摘要

An integral equation-fast Fourier transform (IE-FFT) algorithm is applied to the electromagneticsolutions of the combined field integral equation (CFIE) for scattering problems by anarbitrary-shaped three-dimensional perfect electric conducting object. The IE-FFT with CFIEuses a Cartesian grid for known Green’s function to considerably reduce memory storageand speed up CPU time for both matrix fill-in and matrix vector multiplication when usedwith a generalized minimal residual method. The uniform interpolation of the Green’s functionon an equally spaced Cartesian grid allows a global FFT for field interaction terms. However, thenear interaction terms do not take care for the singularity of the Green’s function and should beadequately corrected. The IE-FFT with CFIE does not always require a suitable preconditionerfor electrically large problems. It is shown that the complexity of the IE-FFT with CFIE is foundto be approximately O(N~(1.5)) and O(N~(1.5)log N) for memory and CPU time, respectively.