Application of preconditioned CG-FFT technique to method of lines for analysis of the infinite-plane metallic grating

In this paper, both the first Fourier transform (FFT) and the preconditioned CG technique are first introduced into the method lines (MOL) to further enhance the computational efficiency of this semianalytic method. Electromagnetic wave scattering by an infinite-plane metallic grating is used as examples to describe its implementation. For an arbitrary incident wave, the Helmholtz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by the FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution involving the computational complexity O(N log N). The banded diagonal impedance matrix is selected as a preconditioner to speed up the convergence rate of the CG algorithm. Our numerical results show that the PCG-FFT method converges to an accurate solution in a much smaller CPU time.