Application of preconditioned Krylov subspace iterative FFT techniques to method of lines for analysis of the infinite plane metallic grating

摘要

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