| Because of the development in short-pulse radar and ultra-wide band communication, the time-domain integral equation (TDIE) which is applied to analysis of wide-band electromagnetic scattering from complex targets and transient radiation from an arbitrary antenna attracts much attentions. The marching-on-in-time methods (MOT) for solving TDIE are instable and inaccurate, so wide engineering applications are impeded. In this dissertation, stable and accurate solution of time-domain integral equation and its application in wide-band electromagnetic scattering and antennas radiation are studied.Firstly, the time-domain electric field integral equation (TDEFIE), magnetic field integral equation (TDMFIE), and combined field integral equation (TDCFIE) formulations are derived from the time-domain Maxwell's equations. The basic idea that relates to the method of moment (MoM) for solving TDIE and numerical algorithms to solve the linear system are introduced.Following, the causes of the late-time instability of MOT method for solving TDIE are introduced, and it is pointed out that the main cause of late-time stability is the numerical discretization error. The numerical discretization error is decreased by accurately evaluating of time-domain impedance matrix elements, and the late-time instability of MOT method is improved by the implicit MOT method and decreasing the numerical discretization error. Hence, the implicit MOT method for solving TDIE is discussed in detail, the technique which is used to treat the singular integrals arising in the TDIE solving is introduced in detail, and a new scheme for accurate evaluation of time-domain impedance matrix elements is proposed also. Time-domain impedance matrix elements are accurately computed by transforming space-time integral of the source cell to one dimension time convolution and one dimension space analytical integral,and the singular integrals are accurately evaluated. The method is used to evaluate mutual and self-impedance matrix elements in TDEFIE, as well as TDMFIE. Numerical results show that the proposed method insures that the solution of time-domain integral equation using marching-on-in-time method is stable and accurate when the time interval changes in the broad range.Next, wire, surface and surface-wire junction basis functions used in solution of antennas radiation are introduced. The solution of TDIE based wire, surface and surface-wire junction basis function is derived in detail and formulations of their time domain impedance matrix elements are presented. The method which is used to treat the singular integrals arising from surface-wire junction basis function is proposed. The method consists of two steps: Duffy transform (treatment of the Green function singularity) and polar coordinate transform (treatment of the singularity in the junction of wire and surface). Feed model and input impedance's computation of antennas are studied. Numerical results show that radiation problems of antennas including wire antenna, surface antenna, wire antenna abrove perfectly conducting bodies and wire antenna mounted on perfectly conducting bodies are stably and accurately solved, and the proposed method by which treating of the singular integrals arose from surface-wire junction basis function process is effective and accurate.In the end, Linear-Linear (LL) basis function and its characteristic are introduced. TDIE based LL basis function is derived, and formulations of their time-domain impedance matrix elements are presented. It is also pointed out that the computing efficiency of time-domain impedance matrix elements is enhanced by using the tensor integral. The stability of TDIE based LL basis function is studied. The precision of TDMFIE based LL basis function is compared with TDMFIE based RWG basis function. Numerical results show that TDIE based LL basis function is stably and accurately solved, and TDMFIE and TDCFIE based LL basis function respectively are more precise than TDMFIE and TDCFIE based RWG basis function. |
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