An FFT-based algorithm for efficient computation of Green's functions for the Helmholtz and Maxwell's equations in periodic domains
For researchers in computational electromagnetics and acoustics, this provides a faster method for computing Green's functions in periodic scattering problems, though it is an incremental improvement over existing numerical methods.
The paper proposes an FFT-based fast algorithm to compute quasi-periodic Green's functions for Helmholtz and Maxwell's equations in periodic domains, addressing the slow convergence of series definitions. Numerical examples show the algorithm is competitive when many values are needed.
The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which needs 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 will 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 are needed, the new algorithm is very competitive.