Szegő–Lobatto quadrature rules

Gauss-type quadrature rules with one or two prescribed nodes are well known and are commonly referred to as Gauss–Radau and Gauss–Lobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szeg? quadrature rules are analogs of Gauss quadrature rules for the integration of periodic functions; they integrate exactly trigonometric polynomials of as high degree as possible. Szeg? quadrature rules have a free parameter, which can be used to prescribe one node. This paper discusses an analog of Gauss–Lobatto rules, i.e., Szeg? quadrature rules with two prescribed nodes. We refer to these rules as Szeg?–Lobatto rules. Their properties as well as numerical methods for their computation are discussed.     

Performance and numerical behavior of the second‐order scheme of precise time‐step integration for transient dynamic analysis

Spurious high‐frequency responses resulting from spatial discretization in time‐step algorithms for structural dynamic analysis have long been an issue of concern in the framework of traditional finite difference methods. Such algorithms should be not only numerically dissipative in a controllable manner, but also unconditionally stable so that the time‐step size can be governed solely by the accuracy requirement. In this article, the issue is considered in the framework of the second‐order scheme of the precise integration method (PIM). Taking the Newmark‐β method as a reference, the performance and numerical behavior of the second‐order PIM for elasto‐dynamic impact‐response problems are studied in detail. In this analysis, the differential quadrature method is used for spatial discretization. The effects of spatial discretization, numerical damping, and time step on solution accuracy are explored by analyzing longitudinal vibrations of a shock‐excited rod with rectangular, half‐triangular, and Heaviside step impact. Both the analysis and numerical tests show that under the framework of the PIM, the spatial discretization used here can provide a reasonable number of model types for any given error tolerance. In the analysis of dynamic response, an appropriate spatial discretization scheme for a given structure is usually required in order to obtain an accurate and meaningful numerical solution, especially for describing the fine details of traction responses with sharp changes. Under the framework of the PIM, the numerical damping that is often required in traditional integration schemes is found to be unnecessary, and there is no restriction on the size of time steps, because the PIM can usually produce results with machine‐like precision and is an unconditionally stable explicit method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

一种宽带雷达回波信号模拟器设计

雷达回波信号模拟是雷达系统研制的重要组成部分,通过分析对比三种信号模拟方法各自的特点,根据实际工程背景选择了一种最适合的宽带雷达回波信号模拟器设计方法。该设计方法基于FPGA+AD9957结构,文中首先以固定点目标为例分析了ISAR信号目标回波的特点,然后根据相应的回波信号特点介绍了模拟器的设计思路及模块构成并阐述了基于AD9957的宽带信号生成方式。经实验证明,该回波信号模拟器具有输出带宽大和产生复杂信号的能力,满足工程技术指标要求。     

数字正交FM解调方案门限效应的研究

介绍了FM解调方案的门限效应。针对传统调频解调方案中的解调门限值高以及降低解调门限的方案难以实现的不足,在研究传统模拟调频解调方案的基础上,分析了数字FM解调方案的门限性能。理论推导证明,数字正交FM解调方案的门限效应低于模拟解调方案。因此,可以采用数字正交解调方案降低其解调门限,而不需采用较难设计和控制的反馈系统,这极大地降低了调频系统实现的复杂度。最后计算机仿真的结果显示,该方案比传统模拟解调方案门限约低2dB。     

直接正交上变频调制器的镜频抑制与本振泄漏对消技术研究

镜频干扰和本振泄漏是制约直接正交变频技术在无线通信收发信机中应用的主要技术瓶颈之一.通过分析直接正交上变频调制器中引起镜频干扰和本振泄漏的原因,利用逆向校正方法,给出了一种闭环反馈式正交基带信号预失真数字幅相平衡补偿电路,提出了一种通过调节基带信号的直流偏置实现本振泄漏对消的措施,提高了直接正交上变频器的镜频抑制和本振泄漏对消能力,并给出了在小型化CDMA发射机中的应用实例.     

A space–time discontinuous Galerkin method for linear convection-dominated Sobolev equations

This article presents a space–time discontinuous Galerkin (DG) finite element method for linear convection-dominated Sobolev equations. The finite element method has basis functions that are continuous in space and discontinuous in time, and variable spatial meshes and time steps are allowed. In the discrete intervals of time, using properties of the Radau quadrature rule, eliminates the restriction to space–time meshes of convectional space–time Galerkin methods. The existence and uniqueness of the approximate solution are proved. An optimal priori error estimate in L^∞(H¹) is derived. Numerical experiments are presented to confirm theoretical results.     

Numerical integrations over an arbitrary quadrilateral region

In this paper, double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method. The physical region is transformed into a standard quadrilateral finite element using the basis functions in local space. Then the standard quadrilateral is subdivided into two triangles, and each triangle is further discretized into 4 × n² right isosceles triangles, with area , and thus composite numerical integration is employed. In addition, the affine transformation over each discretized triangle and the use of linearity property of integrals are applied. Finally, each isosceles triangle is transformed into a 2-square finite element to compute new n² extended symmetric Gauss points and corresponding weight coefficients, where n is the lower order conventional Gauss Legendre quadratures. These new Gauss points and weights are used to compute the double integral. Examples are considered over an arbitrary domain, and rational and irrational integrals which can not be evaluated analytically.     

一类Gauss-Jacobi数值求积公式的极限性质

讨论了形如∫aa+h(x-a)βf(x)dx的Gauss-Jacobi求积公式,当积分区间长度趋向于零时,确定了求积公式的余项中介点η的渐近性,并给出了校正公式,比原公式提高了两次代数精度.此外,本文的结论包含了文[3]的结果.     

Numerical evaluation of various levels of singular integrals, arising in BEM and its application in hydrofoil analysis

The sound implementation of the boundary element method (BEM) is highly dependent on an accurate numerical integration of singular integrals. In this paper, a set of various types of singular domain integrals with three-dimensional boundary element discretization is evaluated based on a transformation integration technique. In the BEM, the integration domain (body surface) needs to be discretized into small elements. For each element, the integral I(x^p, x) is calculated on the domain dS. Several types of integrals IB_α and IC_α are numerically and analytically computed and compared with the relative error. The method is extended to evaluate singular integrals which arise in the solution of the three-dimensional Laplace’s equation. An example of the elliptic hydrofoil is performed to study the physical accuracy. The results obtained using both numerical and analytical methods are shown in good agreement with the experimental data.     

Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs

This paper presents the mechanical quadrature methods (MQMs) for solving boundary integral equations (BIEs) of the first kind on open arcs. The spectral condition number of MQMs is only O(h⁻¹), where h is the maximal mesh width. The errors of MQMs have multivariate asymptotic expansions, accompanied with for all mesh widths h_i. Hence, once discrete equations with coarse meshes are solved in parallel, the accuracy order of numerical approximations can be greatly improved by splitting extrapolation algorithms (SEAs). Moreover, a posteriori asymptotic error estimates are derived, which can be used to formulate self-adaptive algorithms. Numerical examples are also provided to support our algorithms and analysis. Furthermore, compared with the existing algorithms, such as Galerkin and collocation methods, the accuracy order of the MQMs is higher, and the discrete matrix entries are explicit, to prove that the MQMs in this paper are more promising and beneficial to practical applications.