Research On The Finite-element Method And Boundary-element Method And Their Hybrid Methods In Electromagnetic Scattering Problems

Finite element method (FEM) is one of the major numerical methods in computational electromagnetics. Duo to its versatility and flexibility, the FEM is capable of modeling complicated boundary structures as well as inhomogeneous materials. Boundary element method (BEM) is an efficient numerical method which is based on FEM and classical boundary integral (BI) equation method. It transforms domain integration into boundary integration and the electromagnetic problem can be treated with one less dimension. Moreover, the BEM can handle unbounded field problems easily. The application of FEM and BEM and their hybrid methods in electromagnetic scattering problems are studied. The main contributions of this dissertation are as follows:1. BEM is used to analysis of discontinuity in waveguides. The BEM in simply connected domain and multiply connected domain are utilized to the analysis of scattering by the discontinuities in a planar dielectric waveguide and multiple dielectric posts in a rectangular waveguide, respectively. It is shown that this method has some advantages over other methods in regard to saving computer memory.2. An efficient method—inward looking approach combined with multifrontal algorithm is proposed for solving linear equations deduced from hybrid FEM/BEM for electromagnetic problems.The coefficient of the equations formed by FEM/BEM is a matrix of partially sparse and partially full. To solve it fast, the matrix is divided into two parts by the inward looking approach. One is a sparse matrix, and the other is a full matrix. The former is solved by the multifrontal method and the latter is solved by Gauss-Jordan method. Using the above technique, the radar cross section by two dimensional multilayer dielectric cylinders, metal cylinders and conducting bodies coated with dielectric are computed. The results demonstrate that its calculation efficiency is much better than that of Gauss method.3.The hybrid FEM/BEM is used for the computation of electromagnetic scattering by a two-dimensional anisotropic inhomogeneous cylinder. The FEM and the BEM are applied for analyze electromagnetic field in the cylinder and external to the cylinder, respectively. Then the boundary conditions are utilized to establish a matrix equation of partially sparse and partially full. The radar cross section of an inhomogeneous anisotropic cylinder and conducting bodies coated with anisotropic dielectric are calculated. Numerical results show that hybrid FEM/BEM is avail and have advantage in analyzing and calculating the EM problem with inhomogeneous and open domain.4. The hybrid approach of FEM combined with domain decomposition method (DDM) is introduced. Overlapping, nonoverlapping DDM are discussed. Waveguide problems are analyzed by DDM/FEM. The original large computation domain is divided into several nonoverlapping subdomains. A fictitious absorbing boundary condition for connecting the subdomains on fictitious boundary is developed according to the actual field distribution in the waveguide to simulate the propagation of wave between adjacent subdomains. The DDM for waveguide problem is proposed. In this way, the required computer memory is greatly reduced.5.The hybrid approach of FEM combined with DDM and BEM is investigated . Electromagnetic scattering of two dimensional anisotropic dielectric cylinder and two-dimensional open cavity filled with multiplayer anisotropic dielectric are analyzed by DDM/FEM/BEM. In order to ensure the field coupling between subdomains, a new transmission condition is proposed.6. The vector FEM combined with boundary integral equation method is applied for the analyses of electromagnetic scattering by three-dimensional open cavity in the case of arbitrary source excitting. The auto-meshing technology is used in discrete cell. The equivalent magnetic current in the aperture are computed when a dipole antenna and a small current link above the cavity, respectively.