The Research On The SPM And FEM For The Scattering From The Random Rough Surface

This dissertataion is mainly about the use of small perturbation method (SPM) andFEM in the electromagnetic scattering from random rough surface and issues related tothis topic. Three mostly used forms of tapered waves are discussed. The range oftapered parameter g is discussed, and proper ranges for all the three tapered waves aregiven. The tapered wave is introduced into the classical SPM to simulate the scatteringfrom1-D random rough surface. Two classical nodes renumbering algorithms for thereduction of matrix bandwidth and profile are studied and discussed. A novel nodesrenumbering algorithm-GPS (Gibbs-Poole-Stockmeyer) algorithm is proposed basedon GPS algorithm. A novel pseudo-peripheral nodes finding algorithm-WDR(width-depth-ratio) algorithm is proposed based on the pseudo-peripheral nodes findingalgorithm in the GPS algorithm. The WDR algorithm replaces the pseudo-peripheralnodes finding algorithm in GPS algorithm and an improved GPSalgorithm-GPS-WDR algorithm is developed. The GPS-WDR algorithm is introducedto FEM/ABC to simulate the scattering from1-D conducting Gaussian random roughsurface, and the far field results are discussed. The main work of the dissertation is:1. The basic theories and the parameters to describe the random rough surface isintroduced-root mean square (rms) height h and correlation length l aremainly introduced. The random rough surface generating method-MonteCarlo method is introduced, and the1-D and2-D random rough surface aregenerated. The relationship between the profile of the rough surface and rmsheight h are discussed, as well as the relationship between profile andcorrelation length l. Three mainly tapered waves–Thorsos tapered wave,spectral domain tapered wave and the angular domain tapered wave aresummarized and introduced. The proper ranges of tapered parameter g for allthe three tapered waves are discussed and given. The derivations of bistaticscattering coefficient under Thorsos tapered wave incident are given.2. The integral equation method, SPM and Monte Carlo method are introduced.A novel analytical method-hybrid SPM is proposed to simulate the scatteringfrom1-D conducting Gaussian random rough surface. The equations for thescattering electric field are derived. The range for the spectral domain variablek xis discussed. The surface field for the scattering field under tapered wave incident is given by hybrid SPM. The approximation equations for hybridSPM with normal incidence are given. The approximation equations havesimpler forms and the accuracy is testified. The varying of the coherent andincoherent waves with the changes of rms height h has been discussed, andthe physical explanation has been given, too.3. The two classical nodes renumbering algorithms-the improved AD algorithmand the GPS algorithm are studied and discussed. The steps of the improvedAD algorithm and GPS algorithm are given. Taking the spherical crownconformal antenna as the model to testify both the algorithms, the results showtheir advantages and disadvantages in the application as the nodesrenumbering algorithm. Two novel nodes renumbering algorithms areproposed-GGPS algorithm and GGPS-WDR algorithm, and the use of thesetwo algorithms can accelerate the speed of solving the stiffness equations inFEM.4. The GPS-WDR is introduced to FEM/ABC, and the combined method is usedto simulate the scattering from a1-D conducting Gaussian random roughsurface. The bistatic scattering coefficient is obtained, and the results arecompared with the bistatic scattering coefficient obtained by MOM to testifyits accuracy. The effect of the varying rms height and the correlation length tobistatic scattering coefficient is discussed. The proper physical interpretation isgiven.