Research And Application Of Time Domain Discontinuous Galerkin Method In Electromagnetic Problems

Numerical calculation methods commonly used in modern computational electromagnetics include Finite Difference Time Domain(FDTD),Method of Moment(MOM),Finite Element Method(FEM),etc.,but these algorithms still have some limitations when calculating complex electromagnetic targets.Discontinuous Galerkin Time Domain(DGTD)method is a new numerical calculation method in computational electromagnetics in recent years.When dealing with multi-scale complex targets,this method has an advantage.Thus,it is considered to be the most promising numerical calculation method in recent years.The time-domain discontinuous Galerkin method uses the first-order Maxwell's rotation equation as its governing equation,based on discontinuous basis functions and weight functions.As a result,data interaction between adjacent cells is achieved in virtue of numerical flux.It also supports regions' decomposition technology,so this algorithm is considered as a very effective method for solving multi-scale problems in computational electromagnetics.The content of this article is the research and application of the discontinuous Galerkin method in the electromagnetic domain.This article is organized as follows :First,the traditional finite difference method and finite element method in time domain are studied.The time-domain discontinuous Galerkin method has advantages in iteration in the time-domain finite difference method and unstructured grid discreteness in the finite element method.It can be approximated as a special finite element method.Before learning the discontinuous Galerkin method in the time domain,these two traditional algorithms are studied to lay the foundation for the subsequent study of the discontinuous Galerkin method in the time domain.At the same time,this article compares the finite difference method and the finite element method with specific examples,and analyzes the advantages and disadvantages of these two traditional algorithms in calculation.Second,the basic theory of discontinuous Galerkin method in time domain is studied.The derivation of its governing equation,region dispersion,basis function selection,numerical flux,and time-domain step formula are discussed.Among them,the basis of functions and numerical fluxes are highlighted,which lays a solid theoretical foundation for the subsequent program implementation of the algorithm.Third,in the specific electromagnetic calculation,the target model needs to be modeled first.A special finite element mesh generator-GMSH is applied in this article to model and segment the specific target,and the differences of specific model in different algorithms are analyzed.Fourth,based on the research on the theory of the discontinuous Galerkin algorithm in the time domain,the discontinuous Galerkin algorithm in the time domain is implemented in FORTRAN language.The algorithm module includes grid cell initialization,excitation source addition,and boundary condition addition.Also,the electromagnetic field is updated and iterated,and finally the data is output.The reliability of the algorithm is verified by examples.