Research On Hybrid Methods Based On Edge-based FEM For The Analyses Of Electromagnetic Scattering And Radiation Problems

Edge-based FEM is an efficient numerical method for the analyses of electromagnetic problems. In contrast to traditional node-based FEM, edge-based FEM has degrees of freedom associated with edges of elements, rather than with nodes. Thus, it can overcome the shortcomings of the node-based FEM, such as spurious modes and the difficulty of satisfing continuity conditions across material interfaces and of treating geometries with sharp edges.The conception of the edge element was firstly proposed by Whitney in 1957. At the beginning of 1980's, Bossavit and Verite put it to practical application to three-dimensional eddy-current problems. In 1987, Barton and Cendes applied the tetrahedral element to three-dimensional magnetic calculation. Since 1990's, J.M.Jin and J.L.Volakis have studied a series of electromagnetic scattering and radiation problems using hybrid techniques based on edge-based FEM.In this dissertation, a number of hybrid techniques based on edge-based FEM, combined with high frenquency techniques and other methods are presented for the analyses of electromagnetic scattering and radiation problems. The following contributions have been made:A novel hybrid technique FEM/PO-PTD is presented based on edge-based FEM. This technique combines the edge-based finite-element method with physical optics (PO) and physical theory of diffraction (PTD). The hybrid technique is applied to compute thescattering fields from the electrically large bodies with cracks and cavities on their surfaces. It is also used to analyze the scattering characteristics of microstrip antennas residing in a cavity mounted on metal objects with finite sizes. Because the FEM approach generates a highly sparse system matrix and the PO and PTD technique could obtain analytic solutions of RCS for the electrically large bodies, it is shown that the hybrid technique has some advantages over other methods in regard to saving computer memory units and CPU time.A hybrid technique of FEM with Boundary Integral (BI) technique is employed firstly for the evaluation of electromagnetic scattering by microstrip fractal patch antennas residing in a cavity. The calculated results show that the electromagnetic scattering of the microstrip fractal patch antennas residing in a cavity depends largely on the driven element rather than on the parasitic fractal elements.Based on Domain Decomposition Method (DDM), a hybrid technique is presented for the analyses of electromagnetic scattering by electrically large bodies with deep cavities. It can alleviate the problem of memory units when applying FEM alone to such objects.The radiation problems of microstrip antennas residing in a cavity are analyzed by the edge-based FEM with perfectly matched layer (PML) absorbing boundary condition (ABC). The computational area is truncated by PML, as a result, the procedure of FEM is simplified and the memory consumption is reduced greatly.In the computation procedure of the above problems, efficient algorithms to perform sparse matrix were applied to saving computer memory units and CPU time. The conjugate gradient method and biconjugate gradient method were applied to solve the sparse systems of generated linear equations.