腔基微带天线的矢量有限元--边界积分方法分析

该文将矢量有限元——边界积分(Edge-Based FE-BI)混合方法用于腔基微带贴片线的辐射特性分析。分别计算了在无阻抗负载和加有阻抗负载两种情况下的输入阻抗，以此验证了该混合方法的正确性；然后计算了贴片天线表面缝隙部分的场分布，验证微带天线分析模型——传输线模型的合理性；最后计算了E面、H面方向图以及相应的交叉极化方向图。     

A hybrid finite element method for scattering and radiation bymicrostrip path antennas and arrays residing in a cavity

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of microstrip patch antennas and arrays residing in a cavity recessed in a ground plane. The technique combines the finite-element and boundary integral methods to formulate a system for the solution of the fields at the aperture and those inside the cavity via the biconjugate gradient method in conjunction with the fast Fourier transform (FFT). By virtue of the finite-element method, the proposed technique is applicable to patch antennas and arrays residing on or embedded in a layered dielectric substrate and is also capable of treating various feed configurations and impedance loads. Several numerical results are presented, demonstrating the validity, efficiency, and capability of the technique     

Electromagnetic scattering by and transmission through athree-dimensional slot in a thick conducting plane

A hybrid numerical technique for a characterization of the scattering and transmission properties of a three-dimensional slot in a thick conducting plane is presented. The technique combines the finite element and boundary integral methods to formulate a system for the solution of the aperture fields and by virtue of the finite element method, it is applicable to inhomogeneously filled slots of arbitrary shape. The numerical implementation is described for the edge-based expansion functions associated with rectangular brick elements, and examples are presented demonstrating the validity, versatility, and capability of the technique. These also provide some understanding of the slots scattering and transmission properties as a function of its geometry and material filling     

Radiation characteristics of cavity backed aperture antennas infinite ground plane using the hybrid FEM/MoM technique and geometricaltheory of diffraction

A technique using the hybrid finite element method (FEM)/method of moments (MoM) and geometrical theory of diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using finite element method (FEM). The EM fields and their normal derivatives required for FEM solution are obtained using: (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region (assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open-ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity-fed circular aperture in a finite rectangular ground plane are verified with experimental results     

电大尺寸开口腔体电磁散射的子结构法研究

将子结构法与矢量有限元法相结合对无限大接地的三维开口腔体的电磁散射特性进行分析.将原尺寸较大的腔体分解成若干个不重叠的子腔体,在各子腔体内应用矢量有限元法进行分析,在原腔体开口面应用边界积分方程描述.通过求解容量矩阵获得子腔体之间连接边界上的场值,可以快速获得腔体开口面上的场值,极大地减少了存储量和计算量,易于对电大尺寸腔体的电磁散射问题进行分析.数值算例验证了该方法的准确性和高效性.     

有限元法与矩量法结合分析背腔天线的辐射特性

采用有限元法与矩量法相结合分析有限导体面上背腔天线的辐射特性。计算中采用一种有效的积分方程及矢量权函数的形式来保证计算精度。在前处理中采用ＡｕｔｏＣＡＤ中的实体造型技术,对目标可方便地进行离散的局部加密,计算机存储空间及计算量明显下降,使本文方法成为对背腔天线辐射总是中有效方法,文中计算了有限导体面上同轴腔及同轴馈电圆形腔的辐射特性,并与已发表的结果进行比较,验证了本文算法的有效性。     

Finite element analysis of electromagnetic scattering from a cavity

A finite element method (FEM) is implemented to compute the radar cross section of a two-dimensional (2D) cavity embedded in an infinite ground plane. The method is based on the variational formulation which uses the Fourier transform to couple the fields outside the cavity and those inside the cavity; hence, the scattering problem can be reduced to a bounded domain. The convergence of the discrete finite element problem is analyzed. Numerical results are presented and compared with those obtained by the standard finite element-Green function method and by the 2D integral equation method.     

A hybrid finite element-boundary integral method for the analysisof cavity-backed antennas of arbitrary shape

An edge-based hybrid finite element-boundary integral (FE-BI) formulation using tetrahedral elements is described for scattering and radiation analysis of arbitrarily shaped cavity-backed patch antennas. By virtue of the finite element method (FEM), the cavity irregularities, the dielectric super/substrate inhomogeneities, and the diverse excitation schemes inside the cavity may be readily modeled when tetrahedral elements are used to discretize the cavity. On the aperture, the volume mesh reduces to a triangular grid allowing the modeling of nonrectangular patches. Without special handling of the boundary integral system, this formulation is typically applicable to cavity-backed antenna systems with moderate aperture size. To retain an O(N) memory requirement, storage of the full matrix due to the boundary integral equation is avoided by resorting to a structured triangular aperture grid and taking advantage of the integral's convolutional property. If necessary, this is achieved by overlaying a structured triangular grid on the unstructured triangular grid and relating the edge field coefficients between the two grids via two narrow banded transformation matrices. The combined linear system of equations is solved via the biconjugate gradient (BICG) method, and the FFT algorithm is incorporated to compute the matrix-vector product efficiently, with minimal storage requirements     

导电平面上三维任意腔体的散射分析

本文利用边界积分法及连接算法分析导电平面上的三维腔体散射。在引入广义导纳矩阵后,可将腔体分为几段,分别用积分方程法计算每段的广义导纳矩阵。然后利用连接算法得到整个腔体的口径导纳矩阵。最后由广义网络原理求解腔体的口径等效磁流及后向散射场。本文方法极大地缓解了计算机内存对腔体尺寸的限制,提高了分析效率,可作为一种机辅设计算法。     

Scattering from apertures in infinite ground planes using FDTD

A scattered field version of FDTD for scattering from an aperture in an infinite ground plane is presented. In this formulation the fields reflected from the infinite ground plane are computed analytically, not as FDTD scattered fields. This is necessary to eliminate scattering from the edges of the ground plane, where it is terminated at the FDTD outer boundary. Also, the fields scattered by the ground plane are usually of much higher amplitude than the desired aperture-scattered fields. In this formulation these fields need not be absorbed by the FDTD outer boundary. This provides more accurate calculation of low amplitude scattering from the aperture. The formulation can include materials in the aperture and on both sides of the infinite ground plane. For example, scattering from an aperture antenna with a dielectric cover backed by an aperture filled with lossy dielectric can be computed with this formulation     

TE scattering by an inhomogeneously filled aperture in a thickconducting plane

The electromagnetic characterization of the transmission and scattering properties of an aperture in a thick conducting plane filled with an inhomogenous composite material for transverse electric polarization is discussed. Of particular interest in this analysis is the introduction of a new technique that combines the finite element and boundary integral methods. To allow the treatment of large apertures, the conjugate gradient method (CGM) and fast Fourier transform (FFT) are also incorporated for the solution of the resulting system. Numerical examples that demonstrate the validity, versatility, and capability of the technique are presented     

Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically “folds” opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile     

Effects of finite ground plane on the radiation characteristics ofa circular patch antenna

An analytical technique to determine the effects of finite ground plane on the radiation characteristics of a microstrip antenna is presented. The induced currents on the ground plane and on the upper surface of the patch are determined from the discontinuity of the near field produced by the equivalent magnetic current source on the physical aperture of the patch. The radiated fields contributed by the induced current on the ground plane and the equivalent sources on the physical aperture yield the radiation pattern of the antenna. Radiation patterns of the circular patch with finite ground plane size are computed and compared with the experimental data, and the agreement is found to be good. The radiation pattern, directive gain and input impedance are found to vary widely with the ground plane size     

Scattering and radiation analysis of three-dimensional cavityarrays via a hybrid finite-element method

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite-element and boundary-integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate-gradient method in conjunction with the fast Fourier transform thus achieving an O(N) storage requirement. By virtue of the finite-element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique     

背腔式微带天线电磁散射分析的FEM/PO-PTD方法

将一种新的混合方法-FEM/PO-PTD方法，应用于分析计算背腔式微带天线的电磁散射特性。通过无穷大接地导体平面上矩形背腔式微带天线的RCS计算，验证了该方法的正确性。在此基础上，计算了两组有限尺寸金属载体上背腔式微带天线的RCS曲线，理论分析与计算结果表明，该混合方法具有计算机内存需求少、计算时间短等优点。     

Ray Optical Electromagnetic Far-Field Scattering Computations Using Planar Near-Field Scanning Techniques

For accurate scattering computations in the far-field of flat finite objects, field based ray optical methods cannot be used directly, since the finiteness of the objects is not considered in the formulations. In this paper, planar near-field scanning techniques are used to overcome this problem. In particular, scattered ray optical fields are first computed in a scanning plane in the near-field region of the involved objects and are transformed into the far-field afterwards using field expansions in terms of spectrum density functions of outgoing waves. Since evanescent waves are avoided in the scanning plane, sampling rates less than lambda₀/2 can be used for restricted angle range around the normal direction to the scanning plane. Reduced accuracy at grazing directions of observation is overcome by combining solutions provided by several scanning planes. The proposed approach is applied in the postprocessing stage of the recently developed hybrid method combining the uniform geometrical theory of diffraction with the finite element boundary integral technique and with the multilevel fast multipole method.     

Optimization of microstrip feed geometry for prime focus reflectorantennas

The radiation characteristics of a circular microstrip antenna are studied numerically. Surface integral equations are used to formulate the problem from the boundary conditions and moment methods are used to reduce the integral equations to a matrix equation. An analytic method is used to design a microstrip feed and to achieve symmetric radiation patterns with low cross polarization and backlobe levels. The backlobe level is reduced by adding a quarter-wavelength choke to the side wall or the ground plane of the antenna and the bandwidth is improved by stacking two layers. The performance of the feed with the reflector antenna is also considered. One of the feeds was fabricated and tested. Satisfactory agreement between the computed results and the measurement data was obtained. The microstrip feed has a very small size which should reduce its blockage of the reflector aperture     

A fast higher-order time-domain finite element-boundary integral method for 3-D electromagnetic scattering analysis

A novel hybrid time-domain finite element-boundary integral method for analyzing three-dimensional (3-D) electromagnetic scattering phenomena is presented. The method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes. To accurately represent the unknown fields, the scheme employs higher-order vector basis functions defined on curvilinear tetrahedral elements. To handle problems involving electrically large objects, the multilevel plane-wave time-domain algorithm is used to accelerate the evaluation of the boundary integrals. Numerical results demonstrate the accuracy and versatility of the proposed scheme.     

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.     

Hybrid finite element-modal analysis of jet engine inlet scattering

With the goal of characterizing jet engine inlets, a hybrid finite element-modal formulation is presented for the analysis of cavities with complex terminations. The finite element method (FEM) is used to find the generalized scattering matrix for an N-port representation of the complex termination. Where N is the number of traveling modes in the cavity. The cavity is assumed to be circular at the termination (engine) but the remainder of the cavity can be of arbitrary cross section. The scattered fields are obtained by tracing the fields back out of the cavity via a high frequency or modal technique with the generalized scattering matrix used in determining the fields at an aperture near the irregular cavity termination. “Proof of concept” results are presented and several issues relating to the implementation of the FEM are addressed. Among these, a new artificial absorber is developed for terminating the FEM mesh and the suitability of edge or node based elements is examined