A Fast Galerkin Time-domain Finite Element Analysis Method For Discontinuous Periodic Structures Containing Dispersive Media

Due to special spatial field distribution and electromagnetic transmission characteristics,periodic structures have broad application prospects in the engineering design,such as frequency selective surfaces,electromagnetic band gap devices,and shielding materials,etc.With the increasing precision,complexity and multi-dielectric integration of the electromagnetic system,the traditional time domain electromagnetic modeling techniques for periodic structures have been challenged.In this paper,in order to achieve accurate modeling and efficient solution of electromagnetic characteristics of periodic structures with complex media and multi-scale problems,a general numerical model for analyzing electromagnetic wave propagation properties of periodic structures with dispersive media is established,and a fast solution scheme for multi-scale targets is proposed.Discontinuous Galerkin finite element time-domain method(DG-FETD)is quite attractive for analyzing the wideband electromagnetic characteristics of periodic structures that contain dispersive materials.For any given dispersive media,the function of its permittivity varying with frequency is expressed as sum of complex conjugate pole-residues pairs.Recursive convolution method is used to deal with the convolution relationship from frequency-time domian conversion.A high-precision time-domain framework is established by combining Runge-Kutta scheme and UPML layers that absorb high order mode,so as to efficiently obtain the wide band information of electromagnetic targets.In order to achieve rapid analysis of multi-scale electromagnetic simulation,space discretization and time difference two improvement measures are put forward in this paper.Firstly,hybrid modeling is adopted to make full use of respective strengths of tetra-hexahedral meshing,which reduces computing time and memory consumption.Traditional explicit time difference methods are limited by stability condition in multi-scale electromagnetic simulation with fine structure.Therefore,a multilevel local time stepping scheme is proposed,using arbitrary high-order derivative(ADER)time difference format which time derivatives are replaced by space derivatives for each sub-region.The global efficiency and numerical accuracy of multi-scale periodic structures electromagnetic simulation are improved.