Efficient singular element for finite element analysis of quasi-TEMtransmission lines and waveguides with sharp metal edges

The FEM presents a slow rate of convergence when it is used in the analysis of quasi-TEM transmission lines or homogeneous waveguides with field singularities. In order to improve this drawback, mesh techniques or vector elements that cope with the singularities can be used. A different solution is to employ scalar singular elements although, most of those that have been used are only compatible with first-order ordinary elements or can only be used with field singularities of order O(r^-1/2) and O(r^-1/3). In this paper, we present an improvement on the rate of convergence of FEM by employing a scalar singular element, which can be utilized for any order of singularity, is compatible with quadratic or higher order standard elements and is also easy to implement in standard finite element codes. Several transmission lines and waveguides with sharp metal edges have been analysed with a reduced number of degrees of freedom that compares well with other FEM approaches. We also show that electromagnetic fields computed using the proposed singular element have very good agreement with the ones theoretically expected from the singular edge condition     

Singular higher order complete vector bases for finite methods

This paper presents new singular curl- and divergence-conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.     

Application of stable FEM-FDTD hybrid to scattering problems

A recently developed, stable, finite-element method (FEM), finite-difference time-domain (FDTD) hybrid that eliminates the staircase approximation of complex geometries is tested by convergence studies for radar cross-sections. For a conducting sphere, 1 dB accuracy in all directions is obtained with nine cells per wavelength, whereas the NASA almond requires a higher resolution of about 15 cells per wavelength. For scatterers with a smooth boundary, the results converge quadratically with the mesh size, but for a horizontally polarized wave incident on the NASA almond, the order of convergence is lower because of singular fields at the tip     

Higher Order Hybrid FEM-MoM Technique for Analysis of Antennas and Scatterers

A novel higher order large-domain hybrid computational electromagnetic technique based on the finite element method (FEM) and method of moments (MoM) is proposed for three-dimensional analysis of antennas and scatterers in the frequency domain. The geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders. The fields and currents on elements are modeled using curl- and divergence-conforming hierarchical polynomial vector basis functions of arbitrary approximation orders, and the Galerkin method is used for testing. The elements can be as large as about two wavelengths in each dimension. As multiple MoM objects are possible in a global exterior region, the MoM part provides much greater modeling versatility and potential for applications, especially in antenna problems, than just as a boundary-integral closure to the FEM part. The examples demonstrate excellent accuracy, convergence, efficiency, and versatility of the new FEM-MoM technique, and very effective large-domain meshes that consist of a very small number of large flat and curved FEM and MoM elements, with $p$-refined field and current distributions of high approximation orders. The reduction in the number of unknowns is by two orders of magnitude when compared to available data for low-order FEM-MoM modeling.      

A new FEM approach for open boundary Laplace's problem

An efficient improved finite element method (FEM) is presented for electromagnetic Laplace's problems with open boundary. The whole infinite domain is divided into a set of infinite elements instead of ordinary finite elements. Since a special FEM discretization and FEM solving procedure are used, it can not only take much less computer memory than that the conventional FEM needs, but also avoid the calculation error introduced by the truncated boundary or absorbing boundary condition used in conventional FEM     

Diffraction of plane waves by a finite array of dielectric-loaded cavity-backed slots on a common ground plane for oblique incidence and arbitrary polarization

Plane-wave diffraction by a finite array of two-dimensional dielectric-loaded cavity-backed slots on a common ground plane is investigated for oblique incidence and arbitrary polarization. The governing system of coupled singular integral/integrodifferential equations is discretized using moment-method-oriented direct singular integral equation methods. Treating all singular integrals analytically via rapidly converging algorithms leads to numerically stable and efficient analytical expressions for all matrix elements. As a result, no numerical integration is required to compute these elements. Several numerical examples are presented to validate the algorithm and illustrate its convergence characteristics. Results are also presented that reveal the possibility of controlling the absorption efficiency by suitably selecting several geometrical and physical parameters of the structure.     

Efficient Analysis of Millimeter Wave Circuit Using Numerical Calibration Technique

In this paper, A numerical technique, called short-open calibration (SOC), in conjunction with edge-based finite element method (FEM) is employed to analyze millimeter wave circuit that can be segmented into two distinct section: static model of feedlines and dynamic model of circuit discontinuity. The derivation of reflection coefficient of 3D discontinuities is arranged in two steps. In the first step, this SOC technique is incorporated into the FEM for mesh truncation of computaional domain. In this way, much faster convergence is achieved for large-sparse linear matrix equations from FEM by this termination than by perfectly matching layers (PML). The field distribution of the dominated mode in uniform feedlines and entire circuit is obtained individually by exciting a pair of even and odd impressed voltages along the struture. In step two, Scattering parameters based on the voltages and current defintion is calculated by integral of electric and magnetic fields. Numerical solutions for a class of planar circuit discontuities are very well compared with those published in the available literatures.     

Improving Conditioning of Electromagnetic Surface Integral Equations Using Normalized Field Quantities

When the surface integral equation method is applied to study electromagnetic scattering by dielectric or composite metallic and dielectric objects, the unknowns, i.e., the electric and magnetic surface current densities, and the elements of the system matrix, are often of the very different scales. As a consequence, the system matrix may have a high (singular value) condition number. An efficient method is presented to balance the unknowns and the integral equations, and the elements of the system matrix, too. The method is based on the use of normalized field quantities and unknowns, and carefully chosen scaling factors. In the case of dielectric and composite objects the condition numbers of the SIE matrices can be reduced with several orders of magnitudes by the developed method. In the case of high contrast objects, or if the frequency is very low, the developed method leads also to a clear improvement on the convergence of iterative solutions     

各向异性材料部分涂覆导体的散射特性研究

利用物理光学法(PO)与有限元法(FEM)混合方法,研究了有各向异性媒质局部涂覆的电大导体目标的电磁散射问题.在有复杂媒质涂覆的电小结构区域采用有限元法,在未涂覆媒质的电大导体区域采用物理光学法结合等效电磁流法.将两部分区域的边界进行消隐处理,考虑耦合效应,并利用共同的等相位面,将不同区域产生的散射场矢量叠加得到总散射场.文中的实例结果与传统的FEM很好的一致,说明了该方法的有效性和精确性.     

Finite-Element Analysis of Ex Vivo and In Vivo Hepatic Cryoablation

Cryoablation is a widely used method for the treatment of nonresectable primary and metastatic liver tumors. A model that can accurately predict the size of a cryolesion may allow more effective treatment of tumor, while sparing normal liver tissue. We generated a computer model of tissue cryoablation using the finite-element method (FEM). In our model, we considered the heat transfer mechanism inside the cryoprobe and also cryoprobe surfaces so our model could incorporate the effect of heat transfer along the cryoprobe from the environment at room temperature. The modeling of the phase shift from liquid to solid was a key factor in the accurate development of this model. The model was verified initially in an ex vivo liver model. Temperature history at three locations around one cryoprobe and between two cryoprobes was measured. The comparison between the ex vivo result and the FEM modeling result at each location showed a good match, where the maximum difference was within the error range acquired in the experiment (< 5 degC). The FEM model prediction of the lesion size was within 0.7 mm of experimental results. We then validated our FEM in an in vivo experimental porcine model. We considered blood perfusion in conjunction with blood viscosity depending on temperature. The in vivo iceball size was smaller than the ex vivo iceball size due to blood perfusion as predicted in our model. The FEM results predicted this size within 0.1-mm error. The FEM model we report can accurately predict the extent of cryoablation in the liver.     

Finite-element analysis of ex vivo and in vivo hepatic cryoablation.

Cryoablation is a widely used method for the treatment of nonresectable primary and metastatic liver tumors. A model that can accurately predict the size of a cryolesion may allow more effective treatment of tumor, while sparing normal liver tissue. We generated a computer model of tissue cryoablation using the finite-element method (FEM). In our model, we considered the heat transfer mechanism inside the cryoprobe and also cryoprobe surfaces so our model could incorporate the effect of heat transfer along the cryoprobe from the environment at room temperature. The modeling of the phase shift from liquid to solid was a key factor in the accurate development of this model. The model was verified initially in an ex vivo liver model. Temperature history at three locations around one cryoprobe and between two cryoprobes was measured. The comparison between the ex vivo result and the FEM modeling result at each location showed a good match, where the maximum difference was within the error range acquired in the experiment (< 5 degrees C). The FEM model prediction of the lesion size was within 0.7 mm of experimental results. We then validated our FEM in an in vivo experimental porcine model. We considered blood perfusion in conjunction with blood viscosity depending on temperature. The in vivo iceball size was smaller than the ex vivo iceball size due to blood perfusion as predicted in our model. The FEM results predicted this size within 0.1-mm error. The FEM model we report can accurately predict the extent of cryoablation in the liver.     

Regular solution of shielded planar transmission lines

The analysis of shielded transmission lines has been completed using a new method: Regular solution of singular integral equation (RSSIE). Here, an integration procedure is adopted and the uniqueness of the fields is determined by the regularity conditions for the solutions of the singular integral equations at the edges of the metal strips. This leads to more rapid convergence of the series solutions, and enables the analysis of any kind of shielded planar transmission line. It is demonstrated that the results obtained by the proposed method are more accurate than those computed by the spectral domain method (SDM) in comparison with the data measured. In some special cases where the results can exactly be obtained, the proposed method gives more accurate values than those calculated by the SDM. Dominant and higher order modes can be calculated effectively and accurately. The investigation of convergence shows that not only dominant mode but also higher order modes converge rapidly. The computer time required by this proposed method decreases considerably in comparison with SDM     

Eigenvalues for ridged and other waveguides containing corners ofangle 3π/2 or 2π by the finite element method

Superelements developed to enable the finite-element method to be used for computing eigenvalues of the Laplacian over domains containing reentrant corners of angle 3π/2 or 2π are discussed. The superelements embody mesh refinement and include basis functions which emulate the singular behavior of the solution at the corner. Being compatible with linear or bilinear elements, the superelements are easily incorporated into standard finite element programs. The method which has been used to compute transverse electric (TE) and transverse magnetic (TM) mode eigenvalues for ridges and other waveguides is described. The results agree well with those obtained using various other methods     

Full-wave analysis of three-dimensional planar structures

An efficient numerical-analytical approach to the analysis of planar and waveguide three-dimensional structures is presented. To maintain high accuracy and fast convergence of solutions, the technique has been based on Galerkin's method in the spectral domain. The following has been achieved: (1) formulation of a diagonalized set of integral equations for problems associated with planar structures on multilayered uniaxial dielectric substrates; (2) development and application of complete orthonormalized sets of basis functions accounting the edge conditions in explicit form; and (3) development of efficient numerical quadratures for evaluating infinite singular integrals and improvement of the convergence of the integrals and series in the matrix elements of the algebraic system     

Reducing the Number of Elements in a Linear Antenna Array by the Matrix Pencil Method

The synthesis of a nonuniform antenna array with as few elements as possible has considerable practical applications. This paper introduces a new non-iterative method for linear array synthesis based on the matrix pencil method (MPM). The method can synthesize a nonuniform linear array with a reduced number of elements, and can be also used to reduce the number of elements for linear arrays designed by other synthesis techniques. In the proposed method, the desired radiation pattern is first sampled to form a discrete pattern data set. Then we organize the discrete data set in a form of Hankel matrix and perform the singular value decomposition (SVD) of the matrix. By discarding the non-principal singular values, we obtain an optimal lower-rank approximation of the Hankel matrix. The lower-rank matrix actually corresponds to fewer antenna elements. The matrix pencil method is then utilized to reconstruct the excitation and location distributions from the approximated matrix. Numerical examples show the effectiveness and advantages of the proposed synthesis method.      

基于正交搜索的粒子群优化测试用例生成方法

针对粒子群优化算法易出现早熟收敛的问题,本文提出一种基于正交搜索的粒子群优化测试用例生成方法.首先,利用奇异值分解来预测种群的进化方向,在其正交方向进行搜索,可避免已搜索过的区域,有助于跳出局部最优;然后,对粒子速度项进行改进,使其与正交方向保持一致,保证种群可持续受到正交方向的影响,有利于减少奇异值分解次数,降低时间消耗;最后,对每代最优个体进行局部搜索,以增强算法局部搜索能力.实验证明,本文方法在覆盖率、运行时间、进化代数等指标上均有优势.     

Finite-element method coupled with method of lines for the analysis of planar or quasi-planar transmission lines

A full-wave analysis incorporating the finite-element method (FEM) and the method of lines (MoL) is presented in this paper to investigate a planar or quasi-planar transmission-line structure containing complex geometric/material features. For a transmission-line structure being considered, the regions containing complex media are modeled by the FEM while those consisting of simple media with simple geometry are analyzed using the MoL. From the field solutions calculated by MoL, the boundary conditions are constructed. The boundary integrals involved in finite-element analysis are then carried out using these boundary conditions. Since the finite-element analysis is employed only in the complex parts of the structures, while other parts are handled by the MoL, this approach not only retains the major advantage of the FEM in simulating complex structures but also becomes more efficient than the conventional finite-element analysis. Good agreement between the calculated results and those reported in the available literature is obtained and thus validates the present approach. Furthermore, proficient computational efficiency of this method is demonstrated by examining its convergence property. Finally, a number of relevant transmission-line structures are analyzed to illustrate the applications of this approach.     

不完全乔列斯基分解共轭梯度法在磁感应成像三维有限元正问题中的应用

磁感应成像(MIT)3维正问题中,直接求解法计算有限元方程组时,计算速度慢且因舍入误差造成计算结果不正确。该文为了解决这一问题,采用不完全乔列斯基分解共轭梯度(ICCG)迭代求解法。基于ANSYS平台建立有限元数值模型,采用ICCG法迭代求解。通过仿真实验获得设定收敛容差的最优值。对仿真结果进行对比,与直接求解法、雅克比共轭梯度(JCG)法相比,ICCG法计算速度快、稳健性高。计算结果表明ICCG法受网格粗细影响小,能够正确求解磁感应成像3维正问题。     

A locally convergent Jacobi iteration for the tensor singular value problem

Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to tensor. In this paper, we showed local convergence of a parallelizable numerical method (based on the Jacobi iteration) for obtaining the singular values and singular vectors of a tensor.     

Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms

The Landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases. The convergence of the Landweber scheme is of both theoretical and practical importance. Using the singular value decomposition (SVD), we derive an iterative representation formula for the Landweber scheme and consequently establish the necessary and sufficient conditions for its convergence. In addition to verifying the necessity and sufficiency of known convergent conditions, we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results. Moreover, it is found that the Landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values. Furthermore, the limits of the Landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.