Application Of Couplied Galerkin Method In Computational Electromagnetics

In this paper,we discuss the numerical algorithm for solving two-dimensional time-harmonic Maxwell equations.The purpose of this study is to develop a new algorithm to solve the computational electromagnetism problem.The numerical algorithms that have been generated include FVM?FEM?DG?HDG and so on.In this paper we used DG-FEM or HDG-FEM to solve the two-dimensional harmonic Maxwell equations.This coupling method is an innovation in existing numerical algorithms.One of the methods used in this paper not only solves the problem of complex shapes and complex boundary conditions,but also solves the problem of electromagnetic fields in nonlinear and complex media.However,when the traditional finite element method is used to solve the problem,it is found that there are some defects in the method,such as the fact that the method is easy to produce spurious solution.The finite element method eventually yields a large sparse matrix,so it takes time to solve it.Another HDG approach in this paper can compensate for the shortcomings of the finite element method.This method has many advantages,it can adapt to complex geometries and non-conforming meshes,High order accuracy,hp-adaptivity and natural parallelism can been achieved by using HDG methods.An additional hybrid variable is putted forward by HDG methods on the faces of the elements.Local solutions can be definite on those faces,then HDG methods produce a linear system in terms of the degrees of freedoms(DOFs)of the additional hybrid variable only.This method compresses the storage space required by the algorithm and improves the speed of solving the equation.The number of globally coupled DOFs is reduced associated to a classical upwind flux-based DG method.It is always the key to new ways to find new ways to meet these advantages and to suppress their shortcomings.In this paper used HDG-FEM to solve the two-dimensional harmonic Maxwell equations.The solution area is divided into two parts,we use HDG or DG methods in high gradients,where solutions are drastically changed,and the smooth solution region we use finite element method.And in their coupled place to use the appropriate transmission conditions.We choose the distribution of the regional nature according to the respective characteristics of the two methods.In this paper,we first give the derivation formula of LDG and FEM coupling,and give the proof of uniqueness of solution,then,we give the theoretical analysis and formula derivation of the couplied Galerkin method for solving the Maxwell equations.Finally,the feasibility of the method is explained by the proof of suitability.