Finite Element Method Research On Electromagnetic Properties Of Periodic Structures

Due to unique electromagnetic properties,periodic structure has been widely used in antenna design,microwave engineering and optical engineering.Some examples are well-known such as waveguide filters,frequency selective surfaces,phased arrays,optical gratings,photonic crystals,and a variety of metamaterials.To fully characterize the unique electromagnetic properties of periodic structures,a numerical analysis of electromagnetic wave interaction with periodic structures is indispensable.Many numerical methods have been developed for such an analysis.Among these methods,the most popular is the moment method,has received most attention in research related to frequency selective surfaces and microstrip phased arrays.The finite-difference time-domain(FDTD)method has also received much attention because of its ability to compute a solution over a broad frequency band.For periodic structures consisting of complex geometries and inhomogeneous media,the finite element method is preferred over the moment and FDTD methods because of its modeling versatility.The finite element method has been developed for many years and can be divided into the finite element method frequency domain(FEM)and the finite element method time domain(FETD).The discontinuous Galerkin finite element time-domain method(DG-FETD)gets used wildly because of its highly parallel and ability to compute a broad frequency band solution.The main content of this paper is to analyze periodic structure by FEM and DG-FETD respectively.In FEM part,general FEM theory,truncation boundary method and volume excitation method are introduced firstly,then the Floquet's principle and periodic boundary condition are applied to the FEM,and derive the general formula in a unit cell,and then at the interface of different media,Robin boundary condition is introduced to make the meshes unconformal.In DG-FETD part,general theory are introduced firstly,then the numerical flux method is introduced into the periodic face,finally dispersive media is analysed with DG-FETD and show some examples to verify the correctness of the algorithm.