Spectral-Element Spectral-Integral (SESI) Method for the 1-D Bloch (Floquet) Periodic Problems With Scatterers Embedded in Multiple Regions of 2-D Layered Media

Abstract

The hybrid spectral-element spectral-integral (SESI) method is developed for the electromagnetic (EM) scattering in 1-D Bloch (Floquet) periodic problems with scatterers embedded in multiple regions of 2-D layered media. The periodic layered medium Green’s function (PLMGF) is derived for the SESI method so that it can simulate EM scattering by horizontally periodic scatterers placed in an arbitrary number of layers. The SESI method is a combination of the spectral-element method (SEM) and the spectral-integral method (SIM). The SEM is applied only in regions with scatterers and has the merits of exponential convergence at a low spatial sampling density, while the SIM serves as an exact radiation boundary condition for the bottom and top boundaries of each SEM region. Therefore, there is no need to discretize the regions with pure layered media; furthermore, the inverses of these SIM matrices are given exactly and explicitly with only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N\log N)$ </tex-math></inline-formula> CPU time. Three numerical experiments are performed to show the accuracy and efficiency of the SESI method.