一种基于高阶矢量基函数的叠层预条件技术

基于六面体的高阶叠层基函数,提出了一种新颖的构造预条件矩阵的方法.该方法基于叠层基函数特有的嵌套性质,利用特殊的编号策略,将由有限元方法导致的系数矩阵分成块矩阵的形式,最后由不完全LU分解(ILU)导出近似的预条件矩阵.结合该预条件技术,发展了一种叠层预条件-GMRES算法,并将该预条件算法用于加速三维腔体散射的矢量有限元/边界积分(FE-BI)矩阵方程的迭代求解,讨论了该预条件算法中块矩阵ILU分解截断门限T_dr对算法的影响.     

基于高阶叠层矢量基函数的时域电磁场 积分方程方法

本文将准正交高阶叠层矢量基函数用于时域电磁场积分方程(TDIE),求解了三维金属目标的时域电磁散射问题.准正交高阶叠层矢量基函数定义在曲面四边形单元上,并且不要求网格为规范网格,给复杂目标的几何建模和电磁建模带来很大方便.在空间上利用伽略金方法、时间上采用点匹配法求解时域电磁场积分方程,并采用隐式时间步进算法,数值计算结果表明了该方法求解时域积分方程的精确性、高效性与稳定性.     

基于MT-SIE法求解电大介质目标电磁散射

介绍了一种用于均匀介质目标电磁散射求解的新型多区域表面积分方程(MT-SIE)方法。不同于传统的用于介质目标散射求解的积分方法,该方法将均匀介质目标分解为内、外2个独立的子区,通过在介质表面强加Robin传输条件来保证电流和磁流的连续性。由于介质目标被分解为内外2个独立的子区,不同的子区允许非共形剖分。相较于传统方法,该方法可以更高效地与多层快速多级子(MLFMA)相结合求解电大尺寸目标。为进一步加速矩阵的迭代求解,提出了一种高斯-赛德尔型预条件技术,可以有效改善矩阵的收敛,加快迭代求解速度。     

三维目标电磁散射的自适应积分方法

应用自适应积分方法并结合邻近组预条件求解三维导电目标的电磁散射.通过建立辅助基函数将三角形分域基函数映射到矩形网格中,并将格林函数离散变换为具有Toeplitz特性的矩阵.用快速傅立叶变换加速迭代求解中的矩阵和矢量相乘,该方法极大的减少了内存需求和CPU时间,其存储量和运算复杂度分别为低于O(N1.5)和O(N1.5logN)量级.应用邻近组预条件技术进一步降低了迭代求解所需的迭代次数.数值结果表明了该方法的准确性和高效性.     

基于高阶四面体矢量元的大规模本征值求解

采用H1(curl)四面体矢量元分析大规模电磁本征值问题。基于基函数分类和单元矩阵分块技术,提出了一种新型的针对高阶四面体矢量元编程的全局编码方法,并结合RCM重排序技术压缩整体矩阵带宽。通过分析一个矩形谐振腔,系统研究了基于不同求解技术的ARPACK本征值求解器的性能,并将其用于分析各种复杂腔体的谐振问题。     

高阶MoM及其与PO的混合法计算电磁散射问题

本文提出了一种新的以高阶矩量法(MoM)与物理光学法相结合的混合法(MoM-PO).该方法采用曲面参数化的离散方法,保证了建模的精确性.计算过程中将散射表面灵活划分为MoM区和PO区,在各自区域可以灵活确定离散单元的大小和密度.MoM区域的高阶矩量法,采用基于Lagrange插值的高阶矢量基函数,结合点匹配技术,比传统的高阶法简单,易于实现.计算结果表明,本文的高阶矩量法及其与物理光学法结合的混合方法能准确有效的计算目标的电磁散射特性.     

雷达天线罩电磁散射特性研究

采用高阶矩量法研究了常见雷达天线罩的电磁散射特性.首先采用双线性表面几何建模技术对天线罩进行面剖分,再依据等效原理在天线罩表面建立电磁积分方程,最后用基于混合域基甬数的高阶矩量法对其离散求解.实例验证,该方法简单易行、结果精确,同时发现天线罩材料的电参数在很大程度上影响了其电磁散射特性.     

基于Nedelec条件的高阶矢量元构造与实现

采用将Nedelec条件和完整多项式形式结合的方法,系统分析了H1(curl)四面体矢量元的Nedelec函数空间,验证了各矢量元与Nedelec函数空间的关系.基于基函数分类和单元矩阵分块技术,实现了高阶矢量元单元矩阵的求解与组合.通过分析一个矩形谐振腔验证了Nedelec矢量元极好的计算性能,并将其用于分析各种不规则、不均匀腔体的谐振问题.     

基于FE-BI的介质粗糙面上方涂覆目标电磁散射特性研究

采用有限元-边界积分（finite element boundary integral,FE-BI）方法研究了介质粗糙面上方涂覆目标的复合电磁散射特性,推导了一维介质粗糙面上方二维涂覆目标电磁散射的FE-BI公式.在仿真中,采用功能强大的有限元方法模拟涂覆目标内部场,对于涂覆目标与粗糙面之间的多重耦合作用则通过边界积分方程方法进行考虑.结合Monte-Carlo方法,数值计算了介质高斯粗糙面上方涂覆圆柱目标的电磁散射,分析了涂层材料介电常数、粗糙面粗糙度以及介质粗糙面介电常数变化对复合模型双站散射系数的影响.数值结果表明,相比于传统矩量法（method of moment,MoM）,本文方法虽然在处理理想导体模型时效率略低,但可以处理MoM难以处理的复杂媒质电磁散射问题,且计算精度较高.     

三维电大目标散射求解的多层快速多极子方法

为进一步提高对电大尺寸目标散射求解的能力,详细研究了多层快速多极子方法.重点设计了用于多层快速多极子方法的各种优化方法包括Morton编号、转移因子修正内插技术与外向波重复存储策略.对于未知量数目为N的三维电磁散射,数值实验显示多层快速多极子方法具有O(NlogN)量级的计算量、O(N)量级的存储量,特别适合求解三维电大尺寸目标的电磁散射.利用该方法在单机(内存1Gb)上成功计算了未知量为25万的电大尺寸目标散射.     

Scattering analysis of a large body with deep cavities

A numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body, coated with inhomogeneous composite materials, with large and deep cavities. This numerical scheme employs the higher order vector finite-element method (FEM) to discretize the fields inside the cavities and coatings and the higher order boundary integral (BI) method to terminate the FEM computational domain. A highly efficient special solver is designed to eliminate the unknowns inside the cavities, which yields a computed relation (CR) matrix over the cavity's aperture between the tangential electric and magnetic fields. This CR matrix is then combined with the finite element-boundary integral (FE-BI) matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain. The resulting system is solved iteratively using a novel preconditioner derived by replacing the BI with a corresponding absorbing boundary condition (ABC).     

Efficient Calculation of Interior Scattering From Large Three-Dimensional PEC Cavities

Higher order finite element-boundary integral (FE-BI) method is a powerful tool to model the electromagnetic (EM) scattering from three-dimensional large, deep, and arbitrarily-shaped cavities. To further understand the higher order FE-BI method and its applications to the modeling of interior scattering from very large practical perfect electric conductor (PEC) cavity structures, two aspects will be discussed in this paper. The first is on the development of a new integration method to accurately handle singular integrals in calculating BI matrix elements resulted from higher order basis functions defined on higher order elements. The second is on the numerical and experimental verifications of the higher order FE-BI code developed and its applications to the study of the effects of cavity shape, termination and aperture coupling on the interior scattering from large PEC cavities     

A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.     

Numerical Simulation of BOR scattering and radiation using a higher order FEM

Numerical simulations of body-of-revolution geometries for scattering and radiation problems are presented. The formulation consists of a finite element-boundary integral (FE-BI) method which is based on a finite element method that uses higher order nodal-based scalar basis functions for the azimuthal field component and higher order edge-based vector basis functions for the transverse field. This formulation, when combined with a symmetric FE-BI hybridization scheme, yields a final system of equations that is more accurate than earlier first-order formulations. Numerical examples are given to demonstrate the accuracy and capabilities of the higher order solution.     

A Novel Hierarchical Two-Level Spectral Preconditioning Technique for Electromagnetic Wave Scattering

A new set of higher order hierarchical basis functions based on curvilinear triangular patch is proposed for expansion of the current in electrical field integral equations solved by method of moments. The hierarchical two-level spectral preconditioning technique is developed for the generalized minimal residual iterative method, in which the multilevel fast multipole method is used to accelerate matrix-vector product. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basis functions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. Numerical experiments indicate that the new preconditioner can significantly reduce both the iteration number and computational time.     

结合高阶矢量FE/BI方法的快速WCAWE计算

将矢量有限元/边界积分混合方法(FE/BI)用于背腔式贴片天线的输入阻抗建模,在FE/BI方法中,采用基于六面体网格(hexahedron)的高阶矢量基函数(higher order vector basis functions)展开未知场分量;结合高阶矢量FE/BI,采用最近发展起来的WCAWE技术(Well-Conditioned Asymptotic Waveform Evaluation)实现了贴片天线输入阻抗的快速计算;WCAWE技术通过正交化的方式获得低阶模型,这种方式避免了Arnoldi等子空间技术增加矩阵尺度的缺点,同时也确保具有比传统的AWE更好的频带展宽特性;关于输入阻抗计算的数值结果将证明WCAWE技术的优势.     

Application of the inner–outer flexible GMRES-FFT method to the analysis of scattering and radiation by cavity-backed patch antennas and arrays

The finite element-boundary integral (FE-BI) method is applied for the analysis of scattering and radiation by cavity-backed patch antenna and arrays. In this investigation, the FE-BI formulations have been implemented using brick element volumes and it allows for a particular use of the efficient FFT-based iterative solver. The inner–outer flexible GMRES algorithm is applied to solve the equation with a higher convergence speed when compared with the standard GMRES algorithm.     

On the formulation of hybrid finite-element and boundary-integralmethods for 3-D scattering

This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method     

Modeling conformal antennas on metallic prolate spheroid surfaces using a hybrid finite element method

In this paper, the hybrid finite element-boundary integral (FE-BI) method appropriate for modeling conformal antennas on doubly curved surfaces is developed. The FE-BI method is extended to model doubly curved, convex surfaces by means of a specially formulated asymptotic dyadic Green's function. The FE-BI method will then be used to examine the effect of curvature variation on the resonant input impedance of a cavity-backed, conformal slot antenna and a conformal patch antenna recessed in a perfectly conducting, electrically large prolate spheroid surface. The prolate spheroid shape provides a canonical representation of a doubly curved mounting surface. The numerical results for conformal slot and patch antennas on the prolate spheroid are compared as a function of curvature and orientation.