Asymptotic simplifications for hybrid BEM/GO/PO/PTD techniques based on a Generalized Scattering Matrix approach

In this paper we describe a new hybrid weak coupling of asymptotic GO/PO/PTD techniques, Boundary Element Methods (BEM) and Finite Element Method (FEM) based on the FACTOPO Domain Decomposition Methodology (DDM). Thus, the modular domain decomposition approach already assessed with exact techniques such as BEM and FEM is conserved, with the utilization of GO/PO/PTD techniques, resulting in an important reduction of CPU time during parametric studies. As the coupling scheme between asymptotic and exact methods is based on the Lorentz reciprocity theorem, the external structure of the large object is considered perfectly conducting. The accuracy and efficiency of this technique is assessed by performing the computation of the diffraction and radiation by several test-objects in a multi-domain way, cross compared with reference integral equation results.     

A comparison of the boundary element and superposition methods

For some time now, the Boundary Integral Equation (BIE) Method or as it is alternately called the Boundary Element Method (BEM) has been hailed as the technique best suited to problems in elasticity and related fields, both for accuracy and efficiency. The authors demonstrate by example that this is not the case. A much simpler and more versatile technique, the Superposition Method (SUP), is introduced and is shown to outperform BEM in both areas. Followed by a discussion of the merits and drawbacks of each method, compact computer programs for both BEM and SUP and numerical results for nine different example problems are presented to support the authors' claim.     

Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation

This paper aims to obtain approximate solutions of the Nonlinear Klein-Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor-corrector scheme to the nonlinearity which appears in the problem. We employ the time stepping scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated.     

复杂目标的近场RCS估算

为了预估复杂目标的近场雷达散射截面(RCS),通过图形电磁计算方法(GRECO)来求得复杂目标远场散射中心的雷达散射截面,采用z-buffer遮挡消隐技术来提取面元远场散射中心的位置,然后给出一种预估复杂目标近场RCS的方法.在雷达天线与目标之间的距离不是太近的情况下,通过仿真目标的远场和近场RCS的分布情况,并对其结果进行比较分析.可以证明该方法计算出来的近场RCS是有效的、准确的,可以应用到实际工程中去分析和解决问题.     

基于外场场强测量的短波天线辐射效率监测

针对短波天线辐射效率难以现场监测的问题,研究一种基于外场场强测量的短波天线辐射效率监测方法。该方法结合天线仿真与测量技术,通过域变换法解析介质半空间位型并矢格林函数,采用RWG矩量法(RWG-MoM)离散平面分层介质C类混合位电场积分方程（MPIE）,得到天线辐射功率的相对分布。测量天线外场场强,得到场点电磁功率面密度作为样本估计天线辐射功率,由辐射功率与输入功率的比值计算得到天线辐射效率。以短波双极天线为例,基于现有的飞艇场强测量平台,进行室外远场场强的测量,实验得到的归一化场强方向图与仿真结果吻合较好,通过该方法计算得到的天线辐射效率与公开文献一致性较好,实现了短波天线辐射效率的监测。     

A fast multigrid solution of boundary integral equations

A new iterative method is developed for solving the boundary integral equation of steady-state potential problems supplied with mixed boundary conditions. Based on this iteration, we define a simple multigrid technique in connection with the Boundary Integral Equation Method. As we show it through an example, this technique seems to be extremely efficient. It is possible to reduce the total computational cost even by one order of magnitude in certain cases. More precisely, it is shown that if the boundary is discretized by N points, the number of arithmetic operations required is proportional to N² while using the traditional Boundary Integral Equation Method, this number is proportional to N³.     

Implementation of a boundary element method on distributed memory computers

In this paper, we analyse and compare different parallel implementations of the Boundary Element Method on distributed memory computers. We deal with the computation of two-dimensional magnetostatic problems. The resulting linear system will be solved using Householder transformation and Gaussian elimination. Experimental results are obtained on a Meiko Computing Surface with 32 T800 transputers.     

A boundary element formulation for the substation grounding design

A Boundary Element approach for the numerical computation of substation grounding systems is presented. In this general formulation, several widespread intuitive methods (such as Average Potential Method (APM)) can be identified as the result of specific choices for the test and trial functions and suitable assumptions introduced in the Boundary Element Method (BEM) formulation to reduce computational cost. While linear and parabolic leakage current elements allow to increase accuracy, computing time is drastically reduced by means of new completely analytical integration techniques and semi-iterative methods for solving linear equations systems. This BEM formulation has been implemented in a specific Computer Aided Design system for grounding analysis developed in the last years. The feasibility of this new approach is demonstrated with its application to a real problem.     

A Matrix-free Two-grid Preconditioner for Solving Boundary Integral Equations in Electromagnetism

In this paper, we describe a matrix-free iterative algorithm based on the GMRES method for solving electromagnetic scattering problems expressed in an integral formulation. Integral methods are an interesting alternative to differential equation solvers for this problem class since they do not require absorbing boundary conditions and they mesh only the surface of the radiating object giving rise to dense and smaller linear systems of equations. However, in realistic applications the discretized systems can be very large and for some integral formulations, like the popular Electric Field Integral Equation, they become ill-conditioned when the frequency increases. This means that iterative Krylov solvers have to be combined with fast methods for the matrix-vector products and robust preconditioning to be affordable in terms of CPU time. In this work we describe a matrix-free two-grid preconditioner for the GMRES solver combined with the Fast Multipole Method. The preconditioner is an algebraic two-grid cycle built on top of a sparse approximate inverse that is used as smoother, while the grid transfer operators are defined using spectral information of the preconditioned matrix. Experiments on a set of linear systems arising from real radar cross section calculation in industry illustrate the potential of the proposed approach for solving large-scale problems in electromagnetism.     

一种具有宽带双极化低散射特征的微带阵列天线

针对阵列天线宽带散射缩减设计进行研究,设计了一种基于无源对消技术的低散射阵列天线,该新型微带阵列天线在宽频带内具有双极化低雷达散射截面（RCS, Radar Cross Section）性能;对基于两种散射性能不同的单元组成阵列的RCS性能进行了理论研究,进行了单元的散射幅度和相位对阵列RCS的影响分析;提出了一种加载T型缝隙的新型微带天线结构,该单元结构的辐射性能与散射性能能够进行独立调控和综合优化,该单元与传统微带贴片单元具有相似的辐射特性,并可在宽频带（带内和带外）内与传统微带单元产生有效相位差;将传统微带单元和加载T型缝隙的新型微带单元组成4×4阵列天线,仿真结果表明,提出的阵列天线在3GHz～7GHz（相对带宽80%）频带内实现了同极化RCS缩减,在3.3GHz～7GHz（相对带宽71.8%）频带内实现了交叉极化RCS缩减,缩减峰值分别为16.3dB和36.3dB,带内RCS缩减均值分别为14.1dB 和17.6dB;与传统微带阵列天线相比,提出的阵列天线增益下降小于0.1dB;提出的微带阵列天线具有高效率辐射和宽频带双极化低散射性能,为低散射阵列天线设计提供了新的思路。     

On the use of a SIMD vector extension for the fast evaluation of Boundary Element Method coefficients

The paper reports in detail a methodology to fully exploit the potential of a SIMD (Single Instruction Multiple Data) vector extension in the evaluation of certain type of integrals, which occur in the numerical solution of a Boundary Integral Equation (BIE) through the Boundary Element Method (BEM). Specifically, we present an algorithm for the fast evaluation of the integral coefficients appearing in the assembly of the BEM system matrices, which represents an extremely time-consuming task. The numerical scheme is tailored to the specific structure of the integrals associated to a wave propagation phenomenon, governed, in the time domain, by the D’Alembert equation. The reason of this choice resides in the critical importance achieved by this class of problems in many engineering applications. In particular, the application framework this work belongs to is the design of environmentally friendly commercial aircraft, for which the regulation and certification restrictions are, nowadays, a key constraint effecting even the conceptual phase of the design process. For the sake of generality, we used here only the basic features of the SIMD vector extension, common to all the specific architectures available on the market. Particular attention is payed to the accuracy-related issues arising from the use of the low-latency approximations of some of the operators involved. The resulting algorithm minimizes the number of operations involving operands belonging to the same register (“horizontal” or “intra-register” operations). Preliminary numerical results reveal a remarkable speed-up of this highly-demanding part of the solution process, close, in most of the cases, to the theoretical peak. Standard multithreading techniques are additionally introduced to further increase the performance on multiprocessors machines.     

The development of the Trefftzian methodology for engineering design analysis

This paper reviews the developments in the Trefftzian Methodology, which have been undertaken by the authors at the University of Sheffield during the past fifteen years and the application of these developments to engineering design analysis. Initially, in the late 1970s, this work concentrated on the Direct Boundary Element Method (DBEM) and the Indirect Boundary Element Method (IBEM). Unfortunately these methods, as they are normally formulated, give rise to singular integrals, which require special mathematical treatment, when the source and field points coincide on the boundary of the component being analysed. These singular integrals can however be eliminated by placing the source boundary outside the domain of the problem being analysed so that the field and source points never coincide. This technique is known as either the Regular Direct Boundary Element Method (RDBEM) or the Regular Indirect Boundary Element Method (RIBEM) In a further development of the RIBEM, based on the Trefftz Method, the continuous distribution of sources is replaced with sources distributed at discrete points on the source boundary. This modified Trefftz Method eliminates the integrations in the solution procedure, it provides a series solution in terms of the fundamental solution of the problem being analysed and is referred to as the Indirect Discrete Boundary Method (IDBM). The emergence of the IDBM provided the opportunity to develop a combined Boundary Element Finite Element technique which enables these methods to be used simultaneously in a single calculation, thereby exploiting their strengths and minimising their weaknesses. A number of case studies will be discussed in the paper to illustrate the developments in the Trefftzian Methodology and its application to engineering design analysis.     

一种微带天线RCS减缩方法研究

针对微带天线辐射性能提高和RCS减缩这一矛盾,寻求一种对辐射性能影响较小的微带天线RCS减缩新方案.分析了几种RCS减缩方法对微带天线辐射性能及其散射特性的影响,给出了一种综合利用微带贴片上缝隙加载、短路针加载及接地板开缝的微带天线RCS减缩新方法.实现了在天线的工作频率保持不变,增益、带宽损失很小的情况下.微带天线RCS在较宽的频带内得到较大幅度的减缩.仿真实验表明该综合方法是一种较好RCS减缩方法,对微带天线隐身技术有重要的借鉴作用.     

Reconfigurable polarization rotation surfaces applied to the wideband antenna radar cross section reduction

A reconfigurable polarization rotation surface (PRS) using chessboard‐like geometry is introduced for the radar cross section (RCS) reduction of a Yagi‐Uda antenna in this article. The reconfigurable PRS reflector can be switched between low‐RCS PRS reflector and metal reflector. When the reconfigurable PRS reflector with ON‐state diodes is used in the Yagi‐Uda antenna, the antenna has a similar radiation characteristic compared with Yagi‐Uda using metal reflector. The PRS reflector can be used to achieve a low‐RCS characteristic reflector by chessboard configuration with OFF‐state diodes. Finally, the status of RCS can be switched according to the working state of diodes. The results show that the radiation performance of the Yagi‐Uda is preserved. The monostatic RCS of the Yagi‐Uda using PRS reflector with OFF‐state diodes can be reduced more than 25 dB.     

Coupling impedance boundary conditions for absorptive structures with spectral finite elements in room acoustical simulations

Models for Fluid Structure Interaction (FSI) in room acoustical calculations are used in many different fields of engineering like automotive industry or civil engineering. In order to obtain the sound field within an acoustic cavity, which is covered by absorptive boundary structures, with its spatial distribution, very often techniques based on Finite Element formulations are used instead of energy methods. In order to reduce the number of degrees of freedom and therefore the numerical effort, a model reduction method, based on a Component Mode Synthesis (CMS), is presented in this article. Macrostructures are assembled out of single substructures applying shape functions at the interfaces. These substructures contain acoustical design elements, like absorbers or resonators. They are calculated separately in the frame of the CMS approach. The acoustic fluid is modeled with the Spectral Finite Element Method (SEM) and coupled with plate-like compound absorbers at interfaces via impedances using Hamilton’s Principle and a Ritz approach. The porous foam in the absorber is modeled with the Theory of Porous Media (TPM) and the impedances are calculated with the help of the Integral Transform Method (ITM). The method for coupling two macrostructures is compared with an analytical solution and the model for the porous absorber is validated via measurements. Finally an example for the coupled system is presented.     

Analysis of inhomogeneous anisotropic viscoelastic bodies described by multi-parameter fractional differential constitutive models

The response to static loads of plane inhomogeneous anisotropic bodies made of linear viscoelastic materials is investigated. Multi-parameter differential viscoelastic constitutive equations are employed, which are generalized using fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plane body element, are two coupled linear fractional evolution partial differential equations in terms of the displacement components. Using the Analog Equation Method (AEM) in conjunction with the Boundary Element Method (BEM) these equations are transformed into a system of multi-term ordinary fractional differential equations (FDEs), which are solved using a numerical method for FDEs developed recently by Katsikadelis. Numerical examples are presented, which not only demonstrate the efficiency of the solution procedure and validate its accuracy, but also permit a better understanding of the response of plane bodies described by different viscoelastic models.     

基于RCS的无源超高频RFID标签识别距离研究*

通过对无源超高频RFID系统中标签功率的获取、传递以及反射的研究,提出了一种基于雷达散射截面(RCS)对标签识别距离进行计算的新方法。采用高频电磁场仿真软件FEKO对不同标签天线进行建模与仿真,计算标签天线在不同负载下的RCS;再结合识别距离表达式计算该标签的最大识别距离,与标签已有的实测参数进行比较,计算结果与实际参数吻合。研究结果证实了该方法对研究标签识别性能具有很好的借鉴意义。     

A novel reconfigurable FSS applied to the antenna radar cross section reduction

Active reconfigurable FSS using pin diode for the antenna radar cross section (RCS) reduction is proposed. The reconfigurable FSS reflector is presented in this article. The proposed reconfigurable FSS reflector is able to be switched between band‐stop FSS with OFF‐state diodes and band‐pass FSS with ON‐state diodes around 3.8 GHz. The using of band‐stop FSS reflector corresponds to the out‐band RCS reduction during radar operating, and the using of band‐pass FSS reflector corresponds to the in‐band RCS reduction during radar nonoperating. Therefore, the state of the antenna scattering can be switched according to the working state of radar. The results show that the reconfigurable FSS reflector can contribute to the switchable RCS reduction between in band and out band of the antenna. The radiation performance of the antenna is preserved when the diodes are ON state. The monostatic RCS of the antenna with FSS reflector with ON‐state diodes can be reduced more than 25 dB at operating band, and the out‐band RCS reduction can be achieved with ON‐state diodes.     

Numerical simulation of a UC–PBG lens for gain enhancement of microstrip antennas

Because of their versatility and ease of fabrication, Uniplanar Compact–Photonic Band Gap (UC–PBG) structures have been recently applied to microstrip antenna design. However, when the PBG structure is embodied on the ground plane of a conventional microstrip antenna, the resulting configuration suffers from strong backward radiation and reduced efficiency. In this article, a combined UC–PBG/ antenna structure is proposed to overcome the aforementioned drawbacks. The performance characteristics of a microstrip antenna positioned below a UC–PBG are examined using CST and Ansoft commercial software packages, which are based on the Finite Integration Technique (FIT) and the Finite Element Method (FEM), respectively. The proposed antenna demonstrates a remarkable improvement in the bore‐sight gain, about 7.8 dBi at 2.64 GHz, compared with the corresponding conventional microstrip antenna and front‐to‐back ratio in excess of 22.8 dBi. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

Aeroacoustic modeling of complex flow problems: I-Domain decomposition method for the reduced wave equation

An accurate and efficient method for solving the wave equation on multi-domains is developed for two-dimensional geometries. In this work we treat Cartesian geometries, but the method may be directly extended to more general geometries. As a first step, the one-dimensional problem is investigated. The wave equation is solved in the Fourier space. Three different numerical discretizations are tested, a Pointwise second-order accurate discretization (PT), and two fourth-order schemes: a Padè approximation (HO), and an Equation Based scheme (EB). A consistent discretization of the non reflecting boundary conditions is proposed, which preserves the overall accuracy of the corresponding interior scheme. For the solution of the linear system, it is shown that the preconditioned ILUT-GMRES method is an appropriate choice. In the multi-domain method, an optimal iterative procedure is described, specifying the correct form of the transmission conditions at the interfaces. The numerical tests confirm that the present multi-domain technique retains the same numerical properties of the single domain method. Finally the single and multi domain methods are extended to the two-dimensional case. Received: 31 January 2001 / Accepted: 30 September 2001