随机粗糙面散射的微扰法及有限元法研究
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摘要
本论文采用微扰法（small perturbation method，SPM）和有限元法（finite elementmethod，FEM）深入系统地研究了随机粗糙面的散射问题以及相关问题。首先总结归纳了现有的应用最广泛的三种锥形波，并讨论了这三种锥形波的锥型因子g的合理取值范围；随后将Thorsos锥形波引入SPM中，并结合Monte Carlo方法生成了混合方法—混合SPM，并利用混合SPM模拟了一维导体粗糙面的近场散射特性；研究了两种经典的用于减小刚度矩阵带宽和外形的结点重编码算法，并基于经典的结点重编码算法—GPS（Gibbs-Poole-Stockmeyer）算法提出了一种新的结点重编码算法—GGPS（Generalized GPS）算法；基于GPS算法中的伪直径端点寻找算法提出了一种新的伪直径端点寻找算法—WDR（width-depth-ratio）算法，用WDR算法替换GPS算法中的伪直径端点寻找算法得到改进版的GPS算法—GPS-WDR算法；将GPS-WDR算法引入FEM/ABC（absorbing boundary condition，ABC）模拟了一维导体高斯随机粗糙面的散射，并讨论了其远场特性。论文主要工作如下：
1.介绍了随机粗糙面建模涉及的理论和描述粗糙表面的统计参量—均方根高度h和相关长度l，介绍了随机粗糙面建模的的蒙特卡罗方法，生成了一维和二维高斯随机粗糙面，并讨论了粗糙面表面的高度起伏与均方根高度h和相关长度l之间的关系；归纳总结了现有的应用最广泛的三种锥形波—Thorsos锥形波（空间域锥形波）、谱域锥形波和角域锥形波，讨论了三种锥形波的锥型因子g的合理取值范围，给出了Thorsos锥形波和谱域锥形波入射下双站散射系数的推导过程。
2.介绍了积分方程法、SPM和Monte Carlo法，提出一种用来计算Thorsos锥形波入射下一维导体高斯随机粗糙面的散射场的新的快速模拟算法—混合SPM，推导出了TE锥形波入射下的电场散射波公式。采用高斯随机粗糙面模拟微粗糙面，讨论了方法中涉及到的近场表达式的积分方程中的谱域变量k x的有效范围。通过数值计算得到了TE极化散射电场的表面电场结果。给出了垂直入射下混合SPM的近似公式，具有更简单的形式，并且数值精确度与矩量法（Method of Moments，MOM）比较后得到了验证。相干波和非相干波随着均方根高度h的变化而变化的规律以及与此相关的物理解释也得到了讨论。
3.研究和讨论了电磁场有限元结点编码优化的两种典型算法：改进的AD（Akhras和Dhatt）算法和GPS算法，给出了实施两种算法的具体措施。以球冠型共形天线模型的网格结点数据作为实际算例，比较了两种算法对该类问题优化效果的优劣。在GPS方法的基础上，提出了两种新的结点重编码方法—GGPS法和GPS-WDR法，给出了算法的理论依据和详细过程，并通过有限元实例验证了GGPS方法和GPS-WDR方法的有效性，提高了FEM刚度矩阵方程的直接法求解速度。
4.将GPS-WDR引入FEM/ABC并应用于模拟一维导体高斯随机粗糙面的散射，有限元的网格模型通过商业软件ANSYS的脚本语言APDL实现，所得到的双站散射系数的数值结果和MOM得到的结果高度吻合，证明了FEM/ABC的准确性，比较了单纯用GPS算法优化刚度矩阵带宽和外形后的矩阵计算时间和利用GPS-WDR优化刚度矩阵后的矩阵计算时间，时间结果显示了后者的时间优越性，讨论了均方根高度h和相关长度l的变化对双站散射系数的影响，并且给出了结果的合理的物理解释。
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.
1.介绍了随机粗糙面建模涉及的理论和描述粗糙表面的统计参量—均方根高度h和相关长度l，介绍了随机粗糙面建模的的蒙特卡罗方法，生成了一维和二维高斯随机粗糙面，并讨论了粗糙面表面的高度起伏与均方根高度h和相关长度l之间的关系；归纳总结了现有的应用最广泛的三种锥形波—Thorsos锥形波（空间域锥形波）、谱域锥形波和角域锥形波，讨论了三种锥形波的锥型因子g的合理取值范围，给出了Thorsos锥形波和谱域锥形波入射下双站散射系数的推导过程。
2.介绍了积分方程法、SPM和Monte Carlo法，提出一种用来计算Thorsos锥形波入射下一维导体高斯随机粗糙面的散射场的新的快速模拟算法—混合SPM，推导出了TE锥形波入射下的电场散射波公式。采用高斯随机粗糙面模拟微粗糙面，讨论了方法中涉及到的近场表达式的积分方程中的谱域变量k x的有效范围。通过数值计算得到了TE极化散射电场的表面电场结果。给出了垂直入射下混合SPM的近似公式，具有更简单的形式，并且数值精确度与矩量法（Method of Moments，MOM）比较后得到了验证。相干波和非相干波随着均方根高度h的变化而变化的规律以及与此相关的物理解释也得到了讨论。
3.研究和讨论了电磁场有限元结点编码优化的两种典型算法：改进的AD（Akhras和Dhatt）算法和GPS算法，给出了实施两种算法的具体措施。以球冠型共形天线模型的网格结点数据作为实际算例，比较了两种算法对该类问题优化效果的优劣。在GPS方法的基础上，提出了两种新的结点重编码方法—GGPS法和GPS-WDR法，给出了算法的理论依据和详细过程，并通过有限元实例验证了GGPS方法和GPS-WDR方法的有效性，提高了FEM刚度矩阵方程的直接法求解速度。
4.将GPS-WDR引入FEM/ABC并应用于模拟一维导体高斯随机粗糙面的散射，有限元的网格模型通过商业软件ANSYS的脚本语言APDL实现，所得到的双站散射系数的数值结果和MOM得到的结果高度吻合，证明了FEM/ABC的准确性，比较了单纯用GPS算法优化刚度矩阵带宽和外形后的矩阵计算时间和利用GPS-WDR优化刚度矩阵后的矩阵计算时间，时间结果显示了后者的时间优越性，讨论了均方根高度h和相关长度l的变化对双站散射系数的影响，并且给出了结果的合理的物理解释。
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.
引文
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