Fast frequency-sweep analysis of microstrip antennas on dispersivesubstrate

A fast technique that combines the method of asymptotic waveform evaluation (AWE) and the hybrid finite-element boundary-integral (FE-BI) method is introduced for the analysis of cavity-backed microstrip patch antennas residing on a dispersive substrate. Numerical examples are given to demonstrate the accuracy and efficiency of the technique     

Implementation and experiments of a hybrid algorithm of theMLFMA-enhanced FE-BI method for open-region inhomogeneouselectromagnetic problems

Although the computational complexity of the finite-element boundary-integral (FE-BI) method is significantly reduced by the multilevel fast multipole algorithm (MLFMA), this MLFMA-enhanced FE-BI solution experiences a very slow convergence for some complex inhomogeneous problems. A hybrid algorithm, combining direct methods with iterative methods, is designed. to speed up the rate of convergence of this MLFMA-enhanced FE-BI solution. This hybrid algorithm is efficiently implemented with the aid of a newly developed package, SuperLU, of the LU decomposition solver. Numerical experiments are performed for scattering by a coated Northrop wing to demonstrate the efficiency of this hybrid algorithm. More importantly, the thorough investigation of the numerical experiments clearly shows the better accuracy, stability, and robustness of this hybrid algorithm over the conventional algorithms     

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.     

Comparison of three FMM techniques for solving hybrid FE-BI systems

By virtue of its low operation count, the application of the fast multipole method (FMM) results in a substantial speed-up of the boundary-integral (BI) portion of the hybrid finite-element/boundary-integral technique, independent of the shape of the BI contour. Previously, various versions of the fast multipole method have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this paper is to provide a comparison of the various FMM approaches on the basis of implementation, CPU time, and accuracy. To gain an appreciation of the differences among the various FMM methodologies, a large portion of the paper is devoted to a discussion of the algorithms at a tutorial level. Flow charts and pseudo-code are also given, at sufficient detail to facilitate their implementation. We present quantitative CPU and memory requirements, using the scattering by a groove as the basis for comparison, and conclude that the FMM can accelerate the BI computation without any significant deterioration in accuracy. A simpler FMM-based algorithm results in a much smaller execution time but has a larger error. However, it turns out that a third algorithm, designated the “windowed” FMM, provides a very good compromise with respect to error and execution time. The paper concludes with the presentation of some three-dimensional applications for which a hybrid FE-BI technique, in conjunction with a fast-integral algorithm, is well suited     

Adaptive finite element-boundary integral analysis for electromagnetic fields in 3-D

This paper presents a complete adaptive finite element-boundary integral (FE-BI) analysis scheme for the time-harmonic, electromagnetic analysis of three-dimensional inhomogeneous scatterers/radiators in free-space. The adaptive scheme is based on an FE-BI formulation which yields electric and magnetic field solutions simultaneously. It employs a posteriori error estimates which exploit the availability of both field solutions and estimates error distributions and global solution quality for the electric and magnetic fields separately. It automatically determines which elements should be refined in order to equi-distribute the estimated error, based on the type of refinement requested (h,p or hp). This automatic determination is based on extrapolating the elemental error estimates. The algorithm terminates when specified tolerance levels are reached by the electric and/or magnetic field global solution quality estimates. The only required user specifications within the algorithm are the termination tolerances and the types of refinements to effect. Results are presented which show that within the scope of the presented error measures significant reductions in computational cost may be achieved. The proposed scheme could be used with other types of error estimates and it could be adapted to other FE or FE-BI formulations.     

高阶FE-BI方法及一种新型的预条件技术

将基于六面体网格的高阶矢量基函数(higher order vector basis function)引入到矢量有限元-边界积分(FE-BI)混合方法中,用于建模带有深腔和狭长缝隙结构三维目标的电磁散射特性;提出了一种新型的预条件技术,用于加速FE-BI系统的迭代求解;给出了结合该预条件技术的GMRES方法求解腔体电磁散射的算例;数值结果证明了高阶FE-BI方法相对于低阶FE-BI方法的优势以及新型预条件技术的有效性.     

有限元\边界元混合算法分析波导裂缝阵列天线

研究了一种分析波导裂缝阵列天线的方法。将有限元-边界元混合算法(FE-BI)应用于波导裂缝阵列天线的计算中,建立理论分析模型,计算波导裂缝上的等效磁流,进而求解整个天线阵列的远场辐射特性。为了检验这种方法的正确性,将所得的数值计算结果与测试值进行了比较,结果表明:FE-BI法可以作为计算波导裂缝阵列天线的一种有效的方法。     

A multiresolution method for simulating infinite periodic arrays

Hierarchical mixed-order tangential vector finite elements (TVFEs) for tetrahedra are attractive for accurate and efficient analysis of a wide class of electromagnetic radiation and scattering problems. They provide versatile geometrical modeling and accurate field representation by allowing combination of lowest and higher order TVFEs. In this letter, the finite-element boundary-integral (FE-BI) method with hierarchical TVFEs for tetrahedra is used for analysis of infinite, doubly periodic antenna arrays. It is shown that accurate prediction of array scanning properties can be obtained by using higher order TVFEs in the regions where large fields and rapid field variations are expected and lowest order TVFEs elsewhere. This is demonstrated in the case of a microstrip patch array     

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.     

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.     

A Single-Boundary Implicit and FFT-Accelerated Time-Domain Finite Element-Boundary Integral Solver

A novel time-domain finite-element boundary integral (FE-BI) solver for analyzing broadband scattering and radiation from free-standing electromagnetically large and perfect electrically conducting platforms supporting inhomogeneous and geometrically intricate structures is presented. The solver has three distinctive features that render it especially attractive for broadband analysis of installed antennas. i) The FE and BI solver components are hybridized using a single-surface interface. ii) The hybrid equations are solved by an implicit time-marching scheme accelerated by an (outer) Jacobi iterative solver that leverages (inner) direct FE and iterative BI solvers. iii) The BI solver component is accelerated by a distributed memory parallel implementation of the time-domain adaptive integral method based on the message-passing interface. The accuracy, late-time stability, and performance of the proposed time-domain FE-BI solver are demonstrated via its application to various scattering and radiation problems; moreover, the solver is used to characterize conformally mounted antennas on several platforms including an aircraft     

RCS of waveguide cavities: a hybrid boundary-integral/modalapproach

A hybrid technique combining the flexibility of the boundary-integral method and the efficiency of the modal approach is presented. The technique is used for analyzing the electromagnetic scattering from open waveguide cavities. The generalized scattering matrices of the arbitrary waveguide discontinuity regions are determined using a boundary-integral equation formulation. The scattering matrix of the composite structure is found by cascading the scattering matrices of individual sections. The radar cross section of the open cavity is then calculated by a reciprocity formulation in conjunction with the Kirchoff's approximation. Excellent agreements with the standard method of moments solution and with experimental data for offset bend structures are found. Examples of cavities with arbitrarily shaped and absorber-coated terminations are also presented     

合元极技术再认识--一种电大复杂目标散射混合计算技术的考察

合元极技术,即混合有限元、边界元、快速多极子技术,是计算电磁学中近年来日益受到关注的一种精确、高效、通用的技术.本文首先将此技术推广应用于既带涂层又带腔的复杂电大目标电磁散射的计算;接着对合元极技术各种算法的计算精度、迭代收敛速度进行了理论和数值实验的分析研究;然后,从通用性和高效性的角度,对作者采用的不对称合元极技术和近来来其他作者提出的对称合元极技术做了分析比较.最后,本文计算了几种复杂目标的散射截面以证实此项技术的高效、通用.     

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.     

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.     

Scattering from a large body with cracks and cavities by the fast and accurate finite-element boundary-integral method

A large body with cracks and cavities is a typical structure widely existing in realistic targets. In this paper, a newly developed fast and accurate finite-element boundary-integral (FA-FE-BI) method is applied to compute scattering by this kind of scatterer. A thorough analysis on this FA-FE-BI numerical technique is presented, clearly demonstrating that this technique has computational complexity O(N log N) and memory requirement O(N) (N is the total number of surface unknowns). An inward-looking approach is employed as a preconditioner to speed up the rate of convergence of iterative solvers for this structure. Under these techniques, a powerful code is developed for this kind of scatterer whose accuracy, efficiency, and capability is well confirmed by various numerical results.     

复杂媒质电磁散射特性的有限元—边界元方法分析

通过有限元-边界元方法分析具有复杂媒质特性目标的电磁散射特性,如各向异性、双各向同性、双各向异性等.该混合方法能够利用有限元灵活地处理散射体内部的复杂材料,利用边界积分方法分析物体的非闭合区域,避免了使用吸收边界条件截断开放区域.通过推导基于有限元法的双各向异性媒质的泛函表达式,实现铁氧体、等离子体、手征等各类复杂媒质的统一建模,使该方法有很强的通用性.数值结果证明:本文发展的有限元-边界元方法对复杂媒质电磁散射问题分析的准确性和有效性.     

A fast time-domain finite element-boundary integral method forelectromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme     

Scattering from planar structures containing small features usingthe adaptive integral method (AIM)

Fast integral equation algorithms such as the adaptive integral method (AIM) have been demonstrated to reduce memory and execution time associated with moment-method solutions for arbitrarily shaped three-dimensional (3-D) geometries. In this paper, we examine the efficiency of AIM in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas. Such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns. AIM with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries. In the latter part of the paper, we demonstrate the application of AIM in connection with a finite-element boundary-integral formulation for cavity-backed antennas     

Surface Interaction Matrices for Boundary Integral Analysis of Lossy Transmission Lines

A method intended to characterize enclosed computational electromagnetic domains in terms of interaction and response of a defined set of surface excitations is described. The finite-element method is used to compute a matrix relating surface current and tangential field in terms of an appropriate basis set such that a coupled solution with a boundary integral formulation is rendered seamless. The proposed method allows for a decoupled finite-element boundary-integral system through use of a discrete-frequency surface interaction matrix, computed in an alternative way, that is still independent of the properties of the background in which the enclosed region resides. The method is applied to per-unit-length resistance and inductance extraction of a variety of multiconductor lossy transmission lines. The primary advantage the proposed method presents for this particular application is reuse of matrices given recurrence of specific conductor cross sections.