The Research On The Numerical Method Of EM Scattering From The Random Rough Surface

The Electromagnetic scattering from randomly rough surfaces has a wide application, such as remote sensing, oceanography, material science, optics and so on.. With the rapid development of the computer technology, numerical methods have become widely popular over the past several decades. In this thesis we have developed three fast and accurate numerical method to analyze EM scattering from 1-D dielectric rough surfaces. 1) First method is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: firstly, it converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); secondly, for HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the RMS slope is not larger than 16°or interestingly when RMS height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum. 2) In chapter four we based on chapter three in combination with the stochastic second degree (SSD) algorithm to improve the convergence performance. 3) In chapter five, we modified the splitting of the impedance matrix, and we use FBM-SA to solve inner iteration instead of GMRES which is used before to further reduce the computational and storage complexity. This method has great improvement in efficiency. For a surface of 256 wavelengths with RMS height of 0.3 wavelength, correlation length of 2.0 wavelength and 16384 unknowns, the method requires 49seconds per realization on a processor of CPU speed of 3.0GHz, however, FBM-SA requires 372 seconds. The roughness ranges from smooth (0.3 wavelength) to extremely rough (5 wavelengths), and the ratio of the RMS height with the correlation length, ranges from 0.15 to 1.5, corresponding to RMS slope from 12 degree to 64.7 degree. This is the only fast and accurate method can handle such big roughness as far as we know.