Research And Application Of Discontinuous Galerkin Integral Equation Method

The research of the scattering problem of multi-scale targets in the complex electromagnetic environment has become one of the interesting research topics in the field of computational electromagnetics(CEM)over the past few years.However,the traditional integral equation methods have lots of shortage in analyzing these problems,including large condition numbers for the matrix system,slow convergence for iterative solvers and so on.To mitigate these difficulties,a new integral equation based on discontinuous Galerkin method(IEDG)is introduced in the dissertation.The dissertation is organized as follows.First,the motivation and background of IEDG are introduced.We briefly overview the development history of IEDG,and review several important milestones among the vast,well-established literature.The contribution of our work is highlighted afterward.Next,we give the setup of our electromagnetic scattering problems via surface integral equations for conductor,dielectric,and conductor-dielectric hybrid targets,and elaborate the Integral equation theory and practical application.Radar cross section(RCS)as one of the most important physical quantities is utilized to demonstrate the accuracy and efficiency of our algorithm,and elaborate the Integral equation theory and practical application.Moment of method(Mo M)is briefly introduced to solve the integral equation,which is one of the most powerful methods.Furthermore,iterative method of electric field,magnetic field and mixed field integral equation numerical solver is developed.Here,in order to solve the multi-scale target electromagnetic scattering problems,a new method named integral method based on discontinuous Galerkin method is deeply studied.This method enlarges both basic functions and test functions from divergence-conformal space into square-integrable space,which is allowed the non-conformal mesh.Due to the local characteristics of its construction,the IEDG method is highly suitable for applying adaptation techniques.More accurate solutions are obtainable by enriching the approximations locally within each element,either through the use of higher order basis functions(p refinement),or subdivide the element into a few smaller ones(h refinement).According from the DDM method,we develop a IEDG-DDM numerical solver.Finally,by combining IEDG and IBC,we proposed a new method called IEDG-IBC for solving the electromagnetic scattering problems of dielectric-coated objects.This method changes the discretized expression of traditional IBC and improves the properties of matrix system,which exhibits its advantages for analyzing targets with multiple impedance boundaries.In the last,we develop a numerical solver to evaluate the accuracy and efficiency of IEDG-IBC.