Spectral-Element Spectral-Integral (SESI) Method for Doubly Periodic Problems With 3-D Scatterers Embedded in Multiple Regions of Layered Media

In this work, a hybrid 3-D spectral-element spectral-integral (SESI) method is developed by combining the spectral element method (SEM) and spectral integral method (SIM) for the fast evaluation of electromagnetic (EM) scattering from double Bloch (Floquet) periodic problems with 3-D scatterers embedded in multiple regions of layered media. This 3-D SESI method is a further extension of the previously developed 2-D SESI method. In the proposed method, the computational domain is divided into several SEM and SIM subdomains, where the subdomains are coupled by Riemann transmission conditions (RTCs) to allow the use of nonconforming meshes for these subdomains. Meanwhile, the 3-D periodic layered medium Green's function (PLMGF) is derived and employed to simulate 3-D structures in layered media without their volumetric discretization. Four numerical experiments show that the developed SIM method is highly efficient and accurate; the SESI method is more efficient than the traditional finite element method (FEM), thus is a promising solver for designing and optimizing frequency selective surfaces (FSSs), metamaterials, and metasurfaces.