Study Of Some Key Problems Of FDTD And TDIE

In this paper, a general FDTD absorbing boundary condition based on Uniaxial Perfect Match Layer (UPML) for dispersive medium models was proposed. Then, the key problems of Time Domain Integral Equation (TDIE) method is studied systematically and deeply. The electromagnetic scatterings of metal targets are computed by TDIE.Based on the theory of UPML absorbing boundary for non-dispersive medium, taking into account the characteristic that relative permittivity of common dispersive media model can be expressed by fractional polynomials of jω. And combing with the Shift Operator Finite Difference Time Domain (SO-FDTD) method, an FDTD absorbing boundary condition available for three kinds of general dispersive medium models, i.e. Debye model, Lorentz model and Drude model, is given. Numerical results of one-, two- and three-dimensional examples that this general absorbing boundary truncated vacuum, dielectric, and a variety of dispersion media are presented. In addition, the absorbing effectiveness of our method and CPML absorbing boundary condition are compared. The numerical results illustrate the generality and the high effectiveness of presented scheme.An implementation, which can save the computer memory of UPML, is given. The characteristics of UPML absorbing boundary are analyzed. And the method of substitute three-dimensional arrays, which used in UPML computation, for two-dimensional arrays reduces the need of computer memory. At last, this method is used to deal with complex problems such as computing the scattering of the underground objects.The details of computation surface current of straight wire and bend wire by time-domain integral equation (TDIE) method are elaborated. The solution of the electric field integral equation with Moment Method in two-dimensional case is discussed. It can be separated into two cases: (1) TM case. Time-domain electric field integral equation is solved by vector potential of 1 order scheme or 0-order derivative scheme. The scalar potential didn't have to be used in this case. (2) TE case. The time-domain electric field integral equation is solved by vector potential of two order derivative scheme. The non-self elements of the impedance matrix and scalar potential is computed by approximation method, while the self elements of the impedance matrix and scalar potential is computed by exact integral formula.Combining with the characteristics of RWG basis functions in triangular patch modeling, the detailed process of using MOM numerical method to solve TDIE of three-dimensional PEC objects is given. Non-singular integral of resistance coefficient matrix and scalar potential are computed by approximation method. And the singular integrals are computed by the precise integration method of converting integral of triangular facets into trilateral loop integral. The surface current density and far-zone scattered field of three-dimensional PEC objects of our method are good agreeing with results of the literature.