Research On Nodal Discontinuous Galerkin Method In Time-Domain Electromagnetic Computation

In the past decade,the Discontinuous Galerkin Time Domain(DGTD)method has become a very active research topic in Computation Electromagnetics(CEM).The DGTD method combines the advantages of the Finite Element Time Domain(FETD)and Finite Volume Time Domain(FVTD).Not only can unstructured discrete grids be used to process complex models and multi-scale structures,but also numerical flux can be used to exchange information between elements to ensure the stability of the scheme.In addition,the DGTD method solves electromagnetic problems by using higher-order basis functions,and the numerical dispersion error is small,accurate and efficient.Since the DGTD method has good theoretical research value and broad application prospects,this paper,based on the summary of existing research results,the basic theory of the DGTD method is analyzed in detail.And the nodal DGTD method and its key technologies based on Maxwell equations are studied and verified.The main contents and innovation points of this paper are as follows:1.This paper is summarized the basic theories and core ideas of DGTD method for various formats existing in the current literature.The solution idea and the key technology of the DGTD method are described in detail,and the specific derivation of the DGTD method for solving Maxwell equations is given.2.The DGTD method is used to calculate and analyze one-dimensional,two-dimensional and three-dimensional electromagnetic problems.The implementation scheme of nodal DGTD method for solving Maxwell equations in one-dimensional,two-dimensional and three-dimensional cases is given and verified.The applications of two commonly used numerical flux schemes(upwind flux and central flux)and common time integration methods(Runge-Kutta method,Leap-Forg method and Verlet method)in DGTD method are analyzed.3.Based on the basic theory of Uniaxial Perfectly Matched Layers(UPML),the core codes of two-dimensional and three-dimensional DGTD methods for solving electromagnetic radiation and scattering problems using UPML truncated boundary are independently developed.The realization scheme of applying electric dipole source and plane wave source in DGTD method is deeply studied.In addition,a new method of applying dipole source based on equivalence principle is proposed and implemented.In order to ensure the numerical stability and improve the computational efficiency of DGTD method,the Local Time Stepping(LTS)method is preliminarily studied.