粗糙面及其与目标复合电磁散射的矩量法研究
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摘要
本论文采用矩量法(Method of Moment, MOM)深入系统地研究了粗糙面及其与目标的复合电磁散射特性。将多区域分解技术引入到一维理想导体粗糙面及其与上方二维理想导体目标复合电磁散射的快速求解中，并基于非均匀有理B样条(Non_Uniform Rational B-Spline, NURBS)曲面建模方式，研究了二维高斯粗糙面的电磁散射特性。论文的主要工作如下
1、针对一维单层粗糙面和一维多层粗糙面电磁散射MOM研究的特点，及其与二维目标复合电磁散射的共通性，给出了一维粗糙面及其与二维目标复合电磁散射MOM研究的系统性理论。
2、为克服电磁波低掠角入射下因模拟粗糙面尺寸过长而导致的未知量个数较多，MOM无法使用的缺陷，基于消息传递接口(Message Passing Interface, MPI)，采用并行FMM分析了低掠角入射下一维粗糙面及其与二维目标的复合电磁散射特性。
3、将多区域分解技术引入到一维理想导体粗糙面及其与上方目标复合电磁散射的快速求解中，详细给出了粗糙面分区的基本原则。
4、将NURBS曲面建模技术引入到二维粗糙面的几何建模中，详细给出了MOM-NURBS即基于NURBS曲面建模采用定义在NURBS曲面片上的屋顶(roof-top)基函数和刀刃型(razor-blade)权函数求解电场积分方程(Electric FieldIntegral Equation, EFIE)的详细过程，并基于NURBS曲面建模，结合并行MOM技术研究了二维理想导体高斯粗糙面的双站电磁散射特性。
5、基于修正勒让德多项式的高阶矢量基函数，采用高阶MOM研究了二维粗糙面的双站电磁散射特性，并根据阻抗矩阵元素的特点给出了离散所得阻抗矩阵优化填充的详细方案及其优势，同时将奇点消去法用于奇异性阻抗矩阵的近似处理中。
In this thesis, the properties of the electromagnetic (EM) scattering from a roughsurface and the composite scattering from a rough surface with a target have beeninvestigated through the method of moment (MOM). The efficient multiregion modelhas been introduced to fastly calculate the EM scattering from a perfectly electricalconducting (PEC) rough surface with or without a PEC target above it. The charactericsof the EM scattering from a2-D Gaussian rough surface have been investigated withgeometric modeling by the Non_Uniform Rational B-Spline (NURBS) surface. Mainworks of this thesis are as following
1. According to the characteristics of the EM scattering from a1-D single-layeredrough surface and a1-D multi-layered rough surface, and the intercommunity of EMscattering from them with a target, several conclusions of calculating the scattering froma1-D rough surface with and without a2-D target through the MOM have been shown.
2. To overcome the defect of the MOM in solving the EM scattering under lowgrazing angle for the long simulated rough surface, based on the message passinginterface (MPI), the parallel Fast Multiple Method (FMM) has been applied to study theproperties of the EM scattering from a1-D rough surface with and without a2-D targetunder low grazing anlge.
3. The efficient multiregion model has been introduced to calculate the EMscattering from a PEC rough surface with or without a PEC target above it. Theprinciple of dividing the rough surface has been presented in detail
4. The NURBS surface has been applied to model the2-D rough surface. TheMOM-NURBS is adopted to solve the electric field integral equation (EFIE) with theroof-top basis function and the razor-blade matching function on the NURBS surface.The parallel MOM has been used to study the properties of EM scattering from a2-DPEC Gaussian rough surfac with geometric modeling by the NURBS surface.
5. The higher order MOM has been adopted to study the properties of the bistaticscattering from a2-D PEC Gaussian rough surface with the modified Legendrepolynomials as the hierarchical higher order basis functions. The optimized processes ingenerating the impedance matrix are presented. The singularity cancellation method hasbeen applied to treat the singular integrals via coordinate transformation.
1、针对一维单层粗糙面和一维多层粗糙面电磁散射MOM研究的特点，及其与二维目标复合电磁散射的共通性，给出了一维粗糙面及其与二维目标复合电磁散射MOM研究的系统性理论。
2、为克服电磁波低掠角入射下因模拟粗糙面尺寸过长而导致的未知量个数较多，MOM无法使用的缺陷，基于消息传递接口(Message Passing Interface, MPI)，采用并行FMM分析了低掠角入射下一维粗糙面及其与二维目标的复合电磁散射特性。
3、将多区域分解技术引入到一维理想导体粗糙面及其与上方目标复合电磁散射的快速求解中，详细给出了粗糙面分区的基本原则。
4、将NURBS曲面建模技术引入到二维粗糙面的几何建模中，详细给出了MOM-NURBS即基于NURBS曲面建模采用定义在NURBS曲面片上的屋顶(roof-top)基函数和刀刃型(razor-blade)权函数求解电场积分方程(Electric FieldIntegral Equation, EFIE)的详细过程，并基于NURBS曲面建模，结合并行MOM技术研究了二维理想导体高斯粗糙面的双站电磁散射特性。
5、基于修正勒让德多项式的高阶矢量基函数，采用高阶MOM研究了二维粗糙面的双站电磁散射特性，并根据阻抗矩阵元素的特点给出了离散所得阻抗矩阵优化填充的详细方案及其优势，同时将奇点消去法用于奇异性阻抗矩阵的近似处理中。
In this thesis, the properties of the electromagnetic (EM) scattering from a roughsurface and the composite scattering from a rough surface with a target have beeninvestigated through the method of moment (MOM). The efficient multiregion modelhas been introduced to fastly calculate the EM scattering from a perfectly electricalconducting (PEC) rough surface with or without a PEC target above it. The charactericsof the EM scattering from a2-D Gaussian rough surface have been investigated withgeometric modeling by the Non_Uniform Rational B-Spline (NURBS) surface. Mainworks of this thesis are as following
1. According to the characteristics of the EM scattering from a1-D single-layeredrough surface and a1-D multi-layered rough surface, and the intercommunity of EMscattering from them with a target, several conclusions of calculating the scattering froma1-D rough surface with and without a2-D target through the MOM have been shown.
2. To overcome the defect of the MOM in solving the EM scattering under lowgrazing angle for the long simulated rough surface, based on the message passinginterface (MPI), the parallel Fast Multiple Method (FMM) has been applied to study theproperties of the EM scattering from a1-D rough surface with and without a2-D targetunder low grazing anlge.
3. The efficient multiregion model has been introduced to calculate the EMscattering from a PEC rough surface with or without a PEC target above it. Theprinciple of dividing the rough surface has been presented in detail
4. The NURBS surface has been applied to model the2-D rough surface. TheMOM-NURBS is adopted to solve the electric field integral equation (EFIE) with theroof-top basis function and the razor-blade matching function on the NURBS surface.The parallel MOM has been used to study the properties of EM scattering from a2-DPEC Gaussian rough surfac with geometric modeling by the NURBS surface.
5. The higher order MOM has been adopted to study the properties of the bistaticscattering from a2-D PEC Gaussian rough surface with the modified Legendrepolynomials as the hierarchical higher order basis functions. The optimized processes ingenerating the impedance matrix are presented. The singularity cancellation method hasbeen applied to treat the singular integrals via coordinate transformation.
引文
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