Fast Analysis For Electromagnetic Properties Of Complex Medium

It has practical and theoretical value to analyze electromagnetic scattering from the complex medium target. Because the constitutive relationships of complex medium are more complicated than other general isotropic medium, their novel electromagnetic properties, which other materials do not have, have attracted increasingly interests of many scholars. Most of these medium are synthetic materials and therefore their electromagnetic analyses require the complex, high-cost and long-cycle technology. However, the application of numerical simulation methods can not only save the costs and the experimental period, but also guarantee the reliability of productions. In recent years, numerical methods have become increasing important with the development of computers and modern science and technologies. In this thesis, bi-isotropic media is studied by use of the method of moment (MoM) and its radar scattering cross section (RCS) is rapidly solved. The numerical results are given to show good agreement with the published data, which validate the proposed algorithm.The MoM is an effective method used to solve electromagnetic scattering problems and it converts the complex electromagnetic boundary value problem into a dense system of linear equations. To solve the linear equations, the generalized minimum residual method (GMRES) except conjugate gradient method (CG) is widely used. But in practice the restarted GMRES (GMRES(m)) instead of the GMRES method is applied to reduce the memory requirement. However, convergence of the GMRES(m) becomes slow because the orthonormal subspace obtained in previous computation is destroyed after iterative restarting. Hence various accelerative techniques are proposed to improve the convergence. The matrix condition is a major factor to affect the convergence of iterative algorithm. The deflated technique can throw off the minimum eigenvalues of the problem to improve the matrix condition number. Therefore, this thesis employs the GMRES with deflated starting (GMRES-DR(m,k)) to iteratively solve matrix equation and its numerical results show that it converges about 1 time faster than GMRES(m). Also, Flexible GMRES (FGMRES) is studied in this paper, and some numerical results validate its efficiency.Preconditioning technology is widely used to improve the convergence of linear equation. This thesis uses a fast algorithm, i.e., multilevel Green's function interpolation method (MLGFIM), to iteratively solve the system of linear equations. In this case, only the near parts of impedance matrix are used to construct the preconditioner. In this thesis, near sparse inverse preconditioner (SAI) is adopted and its numerical results show its good performance. However, each degree of freedom in SAI is coupled to only a few neighbors and this compact support does not allow an exchange of global information. When the exact inverse of the original matrix is globally coupled, adoption of only a few neighbors in SAI lacks global information of the original matrix. Therefore the performance of resultant preconditioner is obviously deteriorated. A spectral preconditioner with a two-step way is introduced to recover global information by removing the effect of some small eigenvalues in magnitude in the SAI preconditioned matrix. The numerical results illustrate its good performance.