采用曲四面体几何建模的高阶矢量有限元方法

对于具有曲面的几何目标电磁场计算,单纯采用基于直线型四面体的高阶矢量有限元已很难体现高阶技术,可以采用粗造网格单元的优势.基于曲四面体(四面体有10个节点)作剖分单元,将高阶矢量有限元法用于具有曲面几何结构目标的电磁场计算.数值实例包括圆柱形金属谐振腔传播常数的计算.计算结果表明,对于曲面结构的电磁建模采用曲四面体单元相对于直线型四面体单元,其高阶基的优势是很明显的.     

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.     

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.     

高阶基函数与低阶基函数的混合建模

 提出一种在采用高阶基函数时将定义在大尺寸单元上的高阶基函数与定义在小单元上的低阶基函数混合使用的方法.该方法可以合理的使用基函数的阶数与个数,得到准确的计算结果,并且较大幅度地提高了计算效率.该方法适用于对复杂结构目标进行精确建模,并同时具有高阶基函数与低阶基函数的优点.     

利用高阶矢量基函数求解时域磁场积分方程

本文利用一种新的高阶矢量基函数求解了三维时域磁场积分方程,该基函数定义在一个曲边三角形贴片上并用拉格朗日插值多项式来表示每一个贴片内的未知电流密度.该基函数的实质就是将拉格朗日插值多项式的插值点选为高斯积分结点,极大地简化和加快了时域积分方程矩量法的繁琐的时间和空间积分运算;另外,该基函数不要求网格为规范网格,给复杂目标的网格剖分带来很大方便.在空间上利用点匹配方法求解了时域磁场积分方程,数值计算结果表明了该方法求解时域积分方程的精确性和高效性.     

用高阶叠层矢量有限元法计算随钻测井的三维电磁响应

用矢量有限元方法对随钻测井的三维地层电磁响应进行了数值仿真。为了提高随钻测井响应的计算效率和精度,采用了高阶叠层矢量基函数,根据场变化快慢的情况,在不同的剖分单元和同一单元的不同方向采用了不同阶数的基函数,有助于减少剖分网格和未知量。采用了基于圆柱坐标下六面体剖分,从而提高了发射、接收线圈、钻铤和井眼边界的几何建模精度。用解析法和数值模式匹配法对有限元计算的结果进行了验证,显示了非常好的吻合,最后仿真了地层倾角对随钻测井响应的影响。     

电磁散射与辐射问题中的混合基函数矩量法

三维散射与辐射问题通常采用电场积分方程(EFIE)结合矩量法(MoM)求解，而基函数是决定矩量法精度和效率的重要因素。本文针对采用三角形网格剖分会引起未知元过多而采用四边形网格剖分会因为网格质量变差而影响计算精度的问题，提出一种基于三角形与四边形混合网格的混合基函数，应用于散射体RCS和天线阻抗特性计算。结果表明，相比于三角形剖分，混合基函数能够在减少未知元个数的同时获得较高的精度；另外也解决了基于单纯四边形网格的基函数在网格质量较差的情况下不能准确模拟表面电荷的问题。     

一种基于Gordon-Hall 方法的DGTD 高阶网格生成技术*

基于六面体的时域间断伽略金方法(Hex-DGTD)要求将计算域划分为一系列互不重叠的六面体子域,通过求解每个子域到标准立方体的映射函数得到各子域内的Jacobian矩阵.然而一般商业软件仅能够将计算域划分为线性或者较低阶数的六面体网格,这种与目标表面近似度较低的六面体将导致DGTD算法中边界条件设置存在误差.文中结合Gordon-Hall方法提出了任意高阶数的网格生成技术,能够更为精确地模拟出目标表面,大幅减小了求解六面体子域映射函数的误差.最后通过算例验证了这种高阶六面体网格生成技术能够在不明显增加计算资源的前提下,较大程度地提升DGTD算法的求解准确度.     

介质散射的双线性高阶叠层基函数矩量法分析

提出了一种基于双线性思想的高阶基函数降低矩量法分析介质目标电磁散射问题时的未知量.论文给出了双线性高阶叠层基函数的构造过程, 并将其应用于介质的面积分方程分析中.数值算例比较了不同阶数时所需未知量以及计算精度, 表明该高阶叠层基函数在满足相同积分方程的计算精度时能比低阶基函数节省未知量.     

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.     

An a posteriori error reduction scheme for the three-dimensionalfinite element solution of Maxwell's equations

The accuracy of the finite element method (FEM) depends on the properties of the mesh which covers the problem geometry. The accuracy can usually be improved by increasing the element density in the mesh or the order of the shape functions in the elements at the expense of a significant increase in computation time. Instead, in this paper an a posteriori error reduction scheme is applied to improve the accuracy in the solution of three-dimensional electromagnetic boundary value problems. In this scheme, first the FEM, solution is generated by the use of lower-order shape functions. Then the numerical error is expressed in terms of higher-order shape functions and calculated on an element-by-element basis from information derived from the FEM solution. Finally, this error is added to the FEM solution to improve its accuracy. The degree of error reduction which is achieved with the application of this scheme is demonstrated by means of several simple electromagnetic boundary value problems     

Plane wave scattering from 2-D perfectly conducting superquadriccylinders

The plane-wave scattering from perfectly conducting two-dimensional cylinders of arbitrary squareness parameter is investigated. A uniform geometrical optics (UGO) solution valid across the smooth caustics generated by the surface poles or zero curvature (inflection) points is developed based on physical optics (PO). The classical geometrical optics solution is modified using a multiplicative transition function that compensates for the caustic singularities and accounts for the complex ray contributions emanating from nonspecular scattering centers located near the surface poles. The transition function is heuristically derived on the basis of the PO radiation integral and involves a generalized (higher-order) form of Airy functions. The resulting UGO solution for the scattered field is simple, easy to apply, and computationally efficient for electrically large cylinders. It compares well with physical optics (numerical integration) and moment-method solutions for both backscatter and limited bistatic configurations     

Parallel in-core and out-of-core solution of electrically large problems using the RWG basis functions

Currently, the problem size that can be solved in reasonable time using the Method of Moments is limited by the amount of memory installed in the computer. This paper offers a new development that not only breaks this memory constraint, but also maintains the efficiency of running the problem in-core. In this paper, highly efficient parallel matrix-filling schemes are presented for parallel in-core and parallel out-of-core integral-equation solvers with subdomain RWG basis functions. The parallel methodology for matrix filling is quite different when using a subdomain basis as opposed to using a higher-order basis. The parallel in-core solver uses memory, which is often expensive and limited in size. The parallel out-of-core solver is introduced to extend the capability of MoM to solve larger problems that can be as large as the amount of storage on the hard disk. Numerical results on several typical computer platforms show that the parallel matrix-filling schemes and matrix-equation solvers introduced here are highly efficient and achieve theoretical predictions. The implementation of these advancements with the widely used RWG basis functions creates a powerful tool for efficient computational electromagnetics solution of complex real-world problems.     

Errors in Projection of Plane Waves Using Various Basis Functions

Basis functions play important roles in computational electromagnetics (CEM). It is interesting to investigate the errors in the projection of the equivalent current of a plane wave using various basis functions. In this work, the projection error of various basis functions is studied. The basis functions involved are the pulse basis function, the triangular basis function, higher-order versions of these basis functions, and the divergence-conforming basis function on rectangular and triangular elements. The projection errors are derived in closed form. The asymptotic expression of the closed form is given. The analytical results are verified by numerical results. The projection error of the pth order one-dimensional (1D) basis is asymptotically inversely proportional to the (p+1)th power of the density of unknowns. Based on the closed-form projection errors in the one-dimensional case, it is found that when the expansion basis is fixed, the application of different testing functions only affects the coefficient of the projection error, rather than the order. Generally, the error of the divergence-conforming basis in the projection of curl-free vectors is less than that of divergence-free vectors.     

Solving large complex problems using a higher-order basis: parallel in-core and out-of-core integral-equation solvers

The future of computational electromagnetics is changing drastically with the new generation of computer chips, which are multi-cored instead of single-cored. Previously, advancements in chip technology meant an increase in clock speed, which was typically a benefit that computational code users could enjoy. This is no longer the case. In the new roadmaps for chip manufacturers, speed has been sacrificed for improved power consumption, and the direction is multi-core processors. The burden now falls on the software programmer to revamp existing codes and add new functionality to enable computational codes to run efficiently on this new generation of multi-core processors. In this paper, a new roadmap for computational code designers is provided, demonstrating how to navigate along with the chip designers through the multi-core advancements in chip design. A new parallel code, using the Method of Moments (MoM) and higher-order functions for expansion and testing, and executed on a range of computer platforms, will illustrate this roadmap. The advantage of a higher-order basis over a subdomain basis is a reduction in the number of unknowns. This means that with the same computer resources, a larger problem can be solved using higher-order basis than using a subdomain basis. The matrix filling for MoM with subdomain basis must be programmed with multiple loops over the edges of the patches to account for the interactions. However, higherorder basis functions, such as polynomials, can be calculated more efficiently with fewer integrations, at least for the senial code. In terms of parallel integral-equation solvers, the differences between these categories of basis functions must be understood and accommodated. If computational codes are not written properly for parallel operation, taking into account the central processing unit (CPU) architecture and operating system, the result will be an extremely inefficient code. The research presented here will show how to take th     

An application of the boundary element method to the magnetic fieldintegral equation

A boundary element method (BEM) for the solution of electromagnetic scattering problems using the magnetic field integral equation (MFIE) is discussed. The discretized form of the MFIE is written in indicial notation with no limitations placed on the order of either the geometric or functional approximation. By considering several different types of boundary elements, it is determined that geometric errors can be significant and degrade the accuracy of the numerical solution. It is shown that a higher-order approximation for the current could significantly improve the accuracy of the numerical solution. The superparametric boundary element in which the geometry was given quadratic approximation and the current was given linear approximation was more efficient than elements using lower-order approximations. The BEM results are compared to the results obtained using the dielectric bodies of revolution (DBR) code     

Investigation of millimeter-wave scattering from frequencyselective surfaces

A comparative numerical and experimental analysis of scattering from dielectric-backed frequency-selective surfaces in W-band (75-110 GHz) was carried out. The examples studied include metal (aluminium), resistive (bismuth), and bismuth-loaded I-pole or linearized Jerusalem cross arrays on fused silica, all of which exhibit a band-stop resonance in W-band as a general feature. The arrays were fabricated using standard photolithographic techniques. The numerical analysis involves the solution of an electric field integral equation using subdomain rooftop basis and testing functions within the framework of the Galerkin testing procedure. The lossy nature of the materials was fully accounted for. A comparative analysis of doubly stacked aluminium I-pole arrays was also performed. The numerical analysis exploits a variant of the cascade method in that the immediately adjacent dielectric layers are included in the construction of the scattering matrix for the frequency selective surface. This allows the higher-order evanescent Floquet modes to decay sufficiently at the dielectric boundaries so they can be ignored in the scattering matrix     

Entire-domain basis MOM analysis of coupled microstrip transmissionlines

A full-wave spectral-domain integral equation formulation is used to analyze coupled open-boundary microstrip transmission lines. A general rigorous formulation is specialized to the case of two identical uniform lines and a method of moments (MOM) solution is implemented. In contrast with earlier subdomain basis MOM solutions, entire-domain basis functions which incorporate appropriate edge conditions for transverse and longitudinal current components are utilized. This allows closed-form evaluation of relevant spatial integrals and results in improved accuracy using far fewer terms. Numerical results in the form of propagation constants and current distributions are presented for the dominant and first two higher-order coupled modes, and compare favorably to results of other techniques     

一种基于高阶矢量叠层基函数去除复杂谐振腔三维有限元仿真中的伪直流模式的新方法

基于高阶矢量叠层基函数,提出了一种去除复杂谐振腔三维有限元仿真中产生的伪直流模式的新方法.该方法可以非常方便、高效地将谐振腔有限元仿真中所有伪直流模式完全去除.利用该方法可以得到一个精确、高效和稳定的有限元本征求解器.该本征求解器在仿真三维复杂谐振腔上和目前流行的电磁场商业软件的本征模求解器相比具有相当的精度并且具有更高的效率.