Discontinuous Galerkin Time Domain Method And Its Applied Research For Electromagnetic Problems

With the advancement of science and technology,electronic systems such as communication and radar are continuously developing towards multi-frequency bands and high integration.Therefore,the research on wideband electromagnetic radiation and scattering characteristics is becoming increasingly important.This paper mainly studies the application of the discontinuous Galerkin time domain(DGTD)method in wideband electromagnetic radiation and scattering.The basic principles and key techniques of DGTD method are introduced,and the correctness and validity of DGTD method are verified through representative electromagnetic examples.Practical numerical examples demonstrate the wide range of applications of DGTD method in electromagnetic domain.Firstly,the basic theory and application of DGTD are discussed in detail.Based on tetrahedral elements and nodal basis functions,the boundary conditions in DGTD such as perfect electric conductor(PEC),perfect magnetic conductor(PMC),and perfect matching layer(PML)are introduced.The excitation sources such as electric dipole,plane wave excitation,and excitation of waveguide are also discussed in detail.In addition,the traditional total field/scattered field(TF/SF)method of plane wave loading is improved to an incident-wave directly loaded(IWDL)method.Compared with traditional TF/SF method,IWDL method eliminates the buffer zone between the total field and scattered field,and restricts the incident wave inside the scatterer surface and the scattered field outside the scatterer surface based on the characteristic of DGTD that there are two sets of unknowns on both sides of the element interface.The outer surface of the scatterer is used as the surface for near-field to far-field extrapolation.IWDL method not only reduces the difficulty of geometric modeling and electromagnetic modeling,but also reduces the number of unknowns and reduces the dispersion error,and improves computational accuracy and efficiency.In addition,the vector basis functions are studied based on tetrahedral elements,and their correctness and accuracy are validated through numerical examples.Memory consumption,CPU time,and accuracy of vector DGTD and scalar DGTD are compared.Secondly,for the purpose of improving computational efficiency,high-order scalar basis functions and vector basis functions on tetrahedral elements are studied.Solvers of2 nd and 3rd order high-order DGTD scalar are developed for scalar nodal basis functions,and solver of 1.5th order DGTD vector is developed for vector basis functions.On the premise of the same computational accuracy,high-order basis functions can be used with larger mesh sizes and larger time-steppings,so DGTD using high-order basis functions can not only reduce the total computational complexity,but also greatly improve the computational efficiency.A series of examples verify the high efficiency and high-precision features of high-order basis functions.Thirdly,for the purpose of further improving computational efficiency,the prism basis function DGTD method is studied for parallel electromagnetic problems,such as rectangular waveguides,rectangular resonant cavities,and cylindrical resonant cavities.DGTD solvers based on hexahedral elements and tri-prism elements are developed.Compared with traditional tetrahedral elements DGTD,both tri-prism elements and hexahedral elements DGTD have larger volume-to-surface area ratios,which allows for larger time-steppings and thus greater efficiency.Hexahedral elements have higher efficiency improvement,but their application is limited to regular structures.However,tri-prisms have better flexibility,so 1st-2nd order mixed,2nd order,and 3rd order triangular prism basis function solvers are developed in this paper,of which the 2nd order 15-points basis function is a new triangular prism basis function.Through numerical examples,it is verified that high-order tri-prism basis functions have significantly improved efficiency compared to traditional tetrahedral and low-order tri-prism basis functions.Finally,based on the DGTD method with tetrahedral nodal basis functions,the research and analysis of complex electromagnetic characteristics of media such as inhomogeneous media,lossy media,and anisotropic media are conducted.For the first time,the electromagnetic characteristics of 9-parameters anisotropic media are studied using the DGTD method.In the conclusion,the entire article is summarized and future work is arranged.