Research On Absorbing Boundary Condition And Its Application On Electromagnetic Scattering

The finite difference time domain method (FDTD) is an important method of computational electromagnetics, It is widely used in electromagnetic field and electromagnetic wave research such as electromagnetic scattering, microwave devices, antennas and electromagnetic compatibility. The optimization method of several commonly used absorbing boundary condition (ABC) of the FDTD method is studied in this thesis. Then it is applied to electromagnetic scattering problems.The principle of the FDTD method is introduced and the numerical stability and numerical dispersion problem are analyzed. Then the principle of Mur's ABC on the basis of the operator of one-way wave and the perfectly matched layer (PML), uniaxial perfectly matched layer (UPML) ABC on the basis of absorbing medium is introduced, The absorption properties of them are analyzed.The application of the total field / scattering field system and the near-to-far-field extrapolation technology in FDTD analysis of electromagnetic scattering problems are introduced in this thesis.In order to use the FDTD method to analyze electromagnetic scattering problems, On the basis of the study of numerical approximation of the operator of one-way wave, the absorption properties of Mur's ABC, Trefethen-Halpern's ABC and Higdon's ABC are compared and analyzed. The shortcoming of present optimized parameters of Higdon's ABC is studied, and the criterion for the calculation of optimized parameters is improved, the optimized parameters of 1 to 3 order Higdon's ABC are calculated based this criterion.The exponential difference scheme of time partial differential in UPML ABC is presented. The reflection coefficient of the exponential difference scheme is much smaller than traditional central difference schemes.On the basis of high-order Taylor central difference theory, the 2N order central difference scheme of space partial differential is presented, combines with time exponential difference scheme, the 2N order exponential difference scheme of UPML ABC is presented, the absorb effect and the numerical stability of this scheme is studied.Finally, the high-order exponential difference scheme of UPML ABC is applied to the calculation of the bistatic radar cross section (RCS) of aircraft nose with different geometry. The results show that bistatic RCS is closely related to the geometry of them, thence the appropriate geometry can improve the stealth effect of aircraft.