| Method of moments (MoM) is one of the most important methods in the computational electromagnetics because of its high computational accuracy, which is the representative of the method of integral equation, and it has developed a variety of fast algorithms, such as the fast multipole method (FMM). FMM is more efficient than the traditional method of moment. However, its computational quantity of wide angle incidence is still large, so the fast multipole method and sensing compressed (CS) are used to calculate the wide angle incidence of the plane structure. Compressive sensing theory is widely used in the field of signal processing. This method needs to construct several new excitation sources, which are rich in various spatial information, and then use the new excitation source to replace the excitation term in the fast multipole matrix equation. The current value of the new excitation source is calculated, and the current value of the whole incident angle is recovered by using the theory of compressive sensing to improve the computational efficiencyWhen analyse the electromagnetic characteristics of the multi-scale complex target, such as ship platforms, aircrafts, radar systems, and etc., it is need to deal with the structure of the wire antenna and the conductor connected, and it is very important to analyze the electromagnetic properties of this kind of targets. When analyse the junction of line and surface, line and body, such as wire antennas and metal conductors are connected to each other, RWG functions have been unable to satisfy the requirements of numerical discretization, so we use linear basis functions, lines and surfaces combined basis functions and RWG functions to discrete wire antennas, connecting points and conductor surfaces. Bacause iterative calculation of wide angle incidence problems of combination of lines and surfaces is large, sensing compressed (CS) is used to calculate the wide angle incidence of the junction. In the theory of compressed sensing, the sparse transformation matrix is optimized, and three kinds of classical sparse transformation bases, such as Legendre bases, Discrete Fourier bases and Fourier bases are used to solve the problem of linear structure with wide angle incidence.On the other hand, the time domain integral equation method is suitable for solving wide band electromagnetic problems, especially for the analysis and study of the transient electromagnetic scattering and radiation characteristics of the perfect conductor.Time domain integral equation theory of Marching-on-in time (MOT) combines the advantages of the integral method and time domain method. The method only need to mesh the surface of the target, which compare with other numerical methods, such as finite element method and time domain finite difference method, the quantity of the unknown is much less. MOT method need to discrete the surface current by time and space at the same time, then the surface current and other parameters are obtained by solving the coefficient of the current. Different targets need different spatial basis functions to spatial discretizate. Higher order basis functions and approximate prolate spheroidal wave functions (APSWF) are selected as the time base functions.The main contribution of this dissertation is summarized as follows:(1) Based on the research of the traditional method of moments, the fast multipole method is applied to the fast solution of the integral equation in the frequency domain. The fast multipole method and sensing compressed (CS) are used to calculate the wide angle incidence of the plane structure. On the basis of the original matrix equation of the fast multipole, the number of observations required for the calculation of the current value of the wide angle is realized. A number of observation current values are firstly obtained, and then use the compressed sensing technology to recover the current value of the whole incident angle so as to improve the calculation efficiency. At the same time, some typical models, such as the sphere model and the cube model are calculated, by which fast calculation of wide angle scattering problems are effectively realized.(2) The study on the wide angle incidence calculation of electromagnetic scattering of complex wires. The electromagnetic scattering problems of wires are solved by using integral equation method, and the surface current of wires is discretized by the linear basis functions. The compressed sensing theory is applied in solving the wide angle incidence calculation of electromagnetic scattering of wires, and then currents over any incident angles can be calculated after only several measurements by using the theory. In the numerical simulations of single wound axial mode helical antenna and four element linear antennas array, fast calculation of scattering problem over a wide angle of wires is finished and several important parameters are obtained. By applying Legendre basis, Fourier basis and discrete cosine transform basis in the new method as the sparse transform basis, numerical results show that the number of times of measurement is different as sparse transform basis changes, so that the fast algorithm can be improved by constructing better sparse transform basis.(3) The study on the wide angle incidence calculation of electromagnetic scattering of the junction between the wire antenna and the PEC. In order to express the spatial distribution of the surface current of the junction, surfaces of the junction are discretized by the RWG spatial basis functions, lines of the junction are discretizated by the linear basis functions and combination parts of the junction are discretizated by lines and surfaces combined basis functions. The compressed sensing theory is applied in solving the wide angle incidence calculation of electromagnetic scattering of the junction, and currents of any incident angles can be calculated after only several measurements by using this method. In the numerical simulation of axial mode helical antenna with a cup ground and parabolic reflector antenna, fast calculation of scattering problem over a wide angle of the junction is finished and several important parameters are obtained. Numerical results show that the number of computation is different as random measurement matrix changes.(4) The study on transient electromagnetic scattering characteristics of complex wires and the junction between wire antennas and the PEC. Based on traditional time domain integral equation method for solving three-dimensional electromagnetic scattering problems, the MOT method is applied to solve the time domain integral equation. From the basic theory of electromagnetic field, the time domain electrical integral equation, the time domain magnetic integral equation and the time domain eletromagnetic field integral equation are derived. The numerical simulation of the conductor cube and the conducting sphere model is carried out, and the validity of the MOT method is verified. When time domain integral equation method is adopted for solving electromagnetic scattering problems of linear antenna models, in order to improve the late-time stability of the marching-on-in time (MOT) method, the approximate prolate spheroidal wave functions (APSWFs) are proposed and used as the temporal basis functions. Unfortunately, the system derived from these temporal basis functions is noncausal. To overcome this problem, the extrapolation scheme should be included to recover the possibility of time marching. The RWG basis function, linear basis function, and lines and surfaces combined basis function are used as the basis function of the junction between the wire antenna and the PEC in the same time. In the numerical simulations of complex wires and the junction between the wire antenna and the PEC, several important parameters such as the transient surface current responses, return-loss (S11), coupling coefficients (S21), and directivities are obtained. Based on these parameters, the analysis of the radiation and mutual coupling problems are performed.
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