AN FFT-BASED ALGORITHM FOR EFFICIENT COMPUTATION OF GREEN'S FUNCTIONS FOR THE HELMHOLTZ AND MAXWELL'S EQUATIONS IN PERIODIC DOMAINS

摘要

The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which need a large number of values of the Green's functions. A significant topic is the scattering problems in periodic domains, where the corresponding Green's functions are quasi-periodic. The quasi-periodic Green's functions are defined by series that converge too slowly to be used for calculations. Many mathematicians have developed several efficient numerical methods to calculate quasi-periodic Green's functions. In this paper, we propose a new FFT-based fast algorithm to compute the 2D/3D quasi-periodic Green's functions for both the Helmholtz equations and Maxwell's equations. The convergence results and error estimates are also investigated in this paper. Further, the numerical examples are given to show that, when a large number of values is needed, the new algorithm is very competitive.