Study Of Tdie Method For Solving Transient Electromagnetic Scattering Problems

Computational electromagnetics provides strong theoretical supports for the study of electromagnetic scattering characteristics.It covers the researches of many numerical algorithms,such as the Finite Difference Time-Domain(FDTD)method,the Method of Moments(Mo M),and the Finite Element Method(FEM),etc.According to different solution domains,numerical methods can also be divided into time domain methods and frequency domain methods.This dissertation mainly focused on the study of the time domain integral equation(TDIE)method and developed some hybrid methods to analyze the transient scattering responses of perfect electrical conductor(PEC)structures and homogeneous dielectric objects.And we are committed to making this method more stable,more efficient and more applicable.The main contribution of this dissertation can be summarized as follows:(1)Starting from the time-varying Maxwell equations,the time domain electric field integral equation(TDEFIE),the time-domain magnetic field integral equation(TDMFIE)and the time-domain mixed field integral equation(TDCFIE)are derived for the transient scattering responses of three-dimensional PEC targets.Then,the explicit marching-on-in-time(MOT)scheme,implicit marching-on-in-time scheme,and marching-on-in-degree(MOD)scheme are presented in detail to solve the time domain integral equation,respectively.(2)In order to solve the transient scattering problem of a three-dimensional homogeneous dielectric target,we derive the time-domain Poggio–Miller–Chang–Harrington–Wu(PMCHW)equation based on the principle of equivalence at first.Then,the equations are solved by MOD method.After that,we introduce the time domain electric field integral equation(TDEFIE)to simulate the dielectric targets,and solve the TDEFIE equation with MOD and an improved MOD method.(3)Based on the marching-on-in-time(MOT)scheme,a surface integral equation discontinuous Galerkin method(SIE-DG)has been proposed for dealing with nonconformal meshed PEC structures with an interior penalty(IP)formulation.There is a stabilization parameter introduced in an additional constraint to ensure the current continuity.Only if the stabilization parameter is chosen in a proper range could the final results be accurate and stable.However,the selection of the parameter is not easy.Here,we propose a discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree(MOD)scheme.By using the weighted Laguerre polynomials as temporal basis functions,our method does not suffer from the late-time instability and converges very fast even when the stabilization parameter varies over a wide range.(4)When dealing with the complex dielectric object,we offen divided it into different parts and mesh them individually.So the nonconformal discretization is offen obtainned.Therefore,based on MOD scheme,we proposed a time-domain discontinuous Galerkin PMCHW integral equation method to simulate electromagnetic pulse(EMP)responses of the dielectric objects.We use the half Rao–Wilton–Glisson(HRWG)basis functions as the spatial basis ones.Both electric and magnetic current continuities between adjacent elements are guaranteed by introducing additional interior penalty terms.Thus,either conformal or nonconformal meshed three-dimensional dielectric structures can be treated.Meanwhile,the weighted Laguerre polynomials are chosen as the temporal basis functions for capturing stable transient scattering responses.(5)For the DG-TDIE-MOD,as a single weighted Laguerre polynomial is chosen as the temporal basis function,their first and second derivatives are a summation over the lower degrees.The final equation contains a lot of summations,making the computational procedure time-consuming.Therefore,we proposed an improved marching-on-in-degree discontinuous Galerkin method to solve the time-domain electric field integral equation.By adopting HRWGs as spatial basis functions,both conformal and nonconformal discretization scattering problems can be simulated accurately.A combination of three weighted Laguerre polynomials is utilized as new temporal basis functions to derive final equations,where some accumulation terms are eliminated.Therefore,the time spent on computing accumulation term during the iterative procedure is reduced significantly,with the total solution process accelerated.