Shell Vector Elements Based Numerical Methods For Electromagnetic Scattering

As the combination of finite element method (FEM) and boundary integral (BI)equation method, the FEM-BI method is suitable for solution of complicatedinhomogeneous dielectric problems, and no absorption boundary condition is requiredin this method. The regions discretized are only the dielectric regions and the surface ofdielectric. Though FEM-BI has a good computational property for compositeconducting body and dielectric, it is deficient for the analysis of conductor structurescoated by thin layer material. This is because plenty of fine meshes will be required formodeling thin layers if using traditional elements like tetrahedral elements and this willlead into a lot of unkowns and cost too much computational time, in many cases, it isimpossible to realize reasonable solution. The shell vector element (SVE) is adegenerated volume element, the volume integration can be easily simplified intosurface integral by using the SVEs, so the total numbers of unknowns are reduced andthe computational efficiency is enhanced greatly. In this dissertation, focusing on singlelayer or multi-layer thin material problems, thin coating conducting bodies, the principleon shell vector element (SVE), combined SVE with the boundary integral method, andfast techniques on solution of matrix equation are investigated extensively.Firstly, as the foundation of research work in this dissertation, the vector finiteelement method is introduced, further the discontinuity problem of rectangle waveguideis investigated. As one typical example, the scattering from three dimensional cavitylocated on infinite ground plane is analyzed by the FEM-BI method. The above workvalidates the correctness of vector FEM and FEM-BI developed by us, builds solid basisfor the following work.For solving the scattering from thin coating problem of single layer material, theSVE method with the BI method is combined into the SVE-BI method. The SVE-BImethod is used to analyze the scattering of the conducting boday coated by single layerand multi-layer thin isotropic material, the conducting body coated by anisotropicmaterial. Because of the specific feature of the SVEs, the SVE-BI has the advantage ofhigh efficiency, high accuracy over other traditional methods. The advantage has beenproved from numerical results shown in this dissertation. Next, for solving three dimensional electromagnetic scattering from multipleconducting bodies coated by thin layer dielectric, a domain decomposition methodbased on hybrid SVE-BI (called as DDM-SVE-BI) is developed. Based on this method,the solving of the finite element equation for each body can be implemented in parallel,so plenty of computational time can be saved.In order to further enhance the efficiency of solving multiple bodies, we developtwo kinds of matrix splitting domain decomposition method, i.e. matrix splitting domaindecomposition method based on the FEM-BI (called as MSDD-FE-BI) and matrixsplitting domain decomposition method based on the SVE-BI method (called asMSDD-SVE-BI). The matrix splitting domain decomposition method is to divide theoriginal matrix in FEM equation into four sub-matrices with the aid of a pre-conditionermatrix, so the results can be attained only by dealing with these four sub-matricesinstead of the original large matrix. In these methods, the solving of the finite elementequation for each body can be implemented in parallel also and it costs less time thanthe one in traditional DDM. MSDD-FE-BI is used to deal with the FEM equationdiscretized by tetrahedral elements, while MSDD-SVE-BI is used to deal with the FEMequation discretized by the shell vector elements.Finally, for solving the electrically large sizes problem, the fast multipole method(FMM) is used to expedite the matrix-vector multiplication in the MSDD-SVE-BImethod. Based on the addition theory, the interaction between observation points andsource points in boundary integral can be realized by aggregation, translation anddisaggregation. The complexity of matrix-vector multiplication is reduced from O(N2)into O(N1.5), here N is the number of unknowns in surface integral equation. It enhancesthe ability of MSDD-SVE-BI for complicated problems.In this dissertation, according to different methods, numerical results are presentedto prove the accurate and efficiency of these methods.