Study On Generalized Transition Matrix For Multi-scale Complex Electromagnetic Systems

This dissertation,based on the idea of domain decomposition,is devoted to studying on the generalized transition matrix method based on the Huygens equivalence principle for the analysis of the electromagnetic scattering and radiation characteristics of multi-scale complex systems.The characteristics of the generalized transition matrix models of the scattering units consisted of metal or homogenous dielectric,the radiation units containing excitation structures,the slotted cavity units are extracted.The generalized surface integral equations combined with the high frequency physical optics method are used to analyze the corresponding scattering and radiation problem of the multi-model system.The main contribution of this dissertation is summarized as follows:1.Based on uniqueness and equivalence principle of the electromagnetic fields,applying the man-set reference surfaces,the scatterers are equivalent to one-port networks.The rotated tangential components of the incident fields and the scattering fields on the reference surface can be related by the derived generalized transition matrix,which efficiently describes the characteristics of the one-port network.Moreover,the generalized surface integral equations are derived to analyze the systems consist of multi-scatterers.The independent extracted generalized transition matrix method possesses the advantages in high compression ratio,high precision and features of reusable,etc.2.The synthetic basis functions are utilized to compress the number of unknowns,based on the extracted generalized transition matrix.On the proper choice of the form of the auxiliary sources and the position of them in the space,the solution spaces can be generated.Based on the concept of degree of freedom,applying the singular value decomposition to the solution spaces of different types,the low ordered RWG basis functions on the reference surface of the generalized transition matrix model are regrouped into high ordered synthetic basis functions.On the premise of accuracy,the synthetic basis functions are applied on the generalized surface integral equations.With the help of the feature of reusable,the number of unknowns is greatly decreased when analyzing the characteristics of the systems with periodic models.3.For the radiation model,containing internal radiation sources or feeding structures,the mapping matrix is proposed to project the information of the internal sources onto the reference surface effectively and completely,in order to characterize the radiation characteristics of the model.The generalized transition matrix model of the radiation element consists of two ports,one is the reference surface and the other one is the feeding port.With this model,the key parameters of the antenna array such as the input impedance of elements are calculated.In the applications of the antenna array when doing the fast beam scanning,the coupling effects between the models do not change with the feeding magnitude and phase enforced at the feeding ports.Hence,the proposed method greatly reduces the engineering complexity and improves the efficiency.4.For the electromagnetic problems of open-ended cavity structures,artificial reference surfaces are applied to seal the slots and/or apertures to separate the cavity into interior domain and exterior domain.Applying special junctions at the transitional connection of the two domains to guarantee the current continuity on the metallic surface,an associated GTM is constructed to extract the characteristics of the interior region of the cavity.With the help of generalized surface integral equations,the problems of cavity array,multi-windows cavities and cavities with internal sources or different internal mediums can be analyzed feasibly and effectively by the proposed approach and it provides effective solutions for the electronic cavity equipment with complex internal structures.5.A hybrid method of generalized transition matrix method and physical optics is proposed.In the new hybrid algorithm,the entire multi-scale system is divided into electrically large area solved by physical optics method and fine parts with complex structures solved by generalized transition matrix method.With the characteristics of physical optics localization in the coupling process,utilizing the set of Fresnel zone to determine the localized region,the proposed method highly reduced the number of unknowns on the electrically large platform.Compared with the use of a single method,the hybrid method effectively improves the computational efficiency.This dissertation systematically and completely studies the generalized transition matrix method and its applications in the multi-scale problems.Through the concept of domain decomposition and the equivalence principle,it provides an efficient numerical solver of integral equations to solve complex multi-scale electromagnetic radiation and scattering problems.