A 3-D precorrected FFT algorithm for electrically large objects in planarly layered media

A three-dimensional (3D) pre-corrected fast Fourier transform (pFFT) is presented for the fast analysis of electromagnetic (EM) scattering from electrically large perfect electrically conducting structures embedded inside a planarly layered medium. The mixed-potential integral equation (MPIE) is used to formulate the problem and the method of moments (MOM) with Rao-Wilton-Glisson (RWG) basis function is employed to solve the integral equation. In order to avoid direct numerical computation of Sommerfeld integrals (SIs), the two-level discrete complex image method (DCIM) is employed to expedite the matrix filling process. In the iterative stage, the pFFT method is further adopted to accelerate the matrix-vector product, since the resulting matrix contains both cyclic convolution and correlation terms after proper splitting. Moreover, the incomplete LU preconditioner is applied to improve the convergence of the matrix equation. Numerical results are presented to show the efficiency and capability of the method.