Eight-node conforming straight-side quadrilateral element with high-order completeness (QH8-C1)

A new eight-node conforming quadrilateral element with high-order completeness, denoted as QH8-C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high-order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8-C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.     

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials

We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05     

辐射型漏泄同轴电缆的设计

总结了漏泄同轴电缆的理论研究现状。围绕使用频带和耦合损耗这两个重要电气参数，讨论辐射型漏泄同轴电缆的设计方法。基于周期性槽孔结构的空间谐波的分析，讨论了抑制高次谐波以拓展使用频带的方法。利用时域有限差分方法和Matlab软件计算耦合损耗。     

高阶统计量地震子波估计建模

本文在反射系数序列为非高斯、平稳和统计独立的随机过程,地震子波为非因果、混合相位的假设条件下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录进行建模,并采用运算代价较小的基于高阶累积量的线性化求解方法——累积量矩阵方程法进行了子波提取和模型适应性的研究。数值模拟结果和实际地震数据处理结果表明:自回归滑动平均(ARMA)模型比滑动平均(MA)模型具有参数节省、模型更为高效的特点;累积量矩阵方程法可以有效地压制加性高斯噪声,但对累积量样本估计的准确性要求较高;如果累积量样本估计的误差和方差适度,结合自回归滑动平均(ARMA)模型描述的累积量矩阵方程法可以高效、准确地估计出地震子波。     

Implicit–Explicit Schemes for BGK Kinetic Equations

In this work a new class of numerical methods for the BGK model of kinetic equations is presented. In principle, schemes of any order of accuracy in both space and time can be constructed with this technique. The methods proposed are based on an explicit–implicit time discretization. In particular the convective terms are treated explicitly, while the source terms are implicit. In this fashion even problems with infinite stiffness can be integrated with relatively large time steps. The conservation properties of the schemes are investigated. Numerical results are shown for schemes of order 1, 2 and 5 in space, and up to third-order accurate in time.     

一种新的高次边缘元方法

讨论了一种新的高次边缘元方法，它不仅消除了伪解，并具有简单高效的特点．着重研究了二次边缘元的空间构造；给出了有关计算公式．对具有精确解的条形介质填充波导主模和高次模本征值的计算表明：二次边缘元方法的计算精度比一次边缘元提高约一个数量级．块状介质填充和衬底各向异性的微带线主模色散曲线的计算证实了该方法的精确性和广泛的适用性．     

一种基于循环小波累积量的谐波恢复方法

循环统计量是乘性和加性噪声中谐波恢复问题的主要分析工具之一。本文在其基础上提出了一种新的理论与方法——基于循环小波累积量的谐波恢复方法。首先,提出了循环小波累积量的定义。然后,建立了基于一阶、二阶、三阶循环小波累积量的谐波分量的频率和相位的估计方法。在此基础上,采用了一种可调参数的小波,通过调节其参数来改善传统方法中频率分辨率低的缺陷。最后给出了模拟实验结果。     

FREQUENCY DOMAIN TESTS OF MULTIVARIATE GAUSSIANITY AND LINEARITY

A stationary multivariate time series { X _t } is defined as linear if it can be written in the form X _t = ∑^∞ _{j =−∞} A _j e _{t − j} where A _j are square matrices and e _t are independent and identically distributed random vectors. If the e _t } are normally distributed, then { X _t is a multivariate Gaussian linear process. This paper is concerned with the testing of departures of a vector stationary process from multivariate Gaussianity and linearity using the bispectral approach. First the definition and properties of cumulants of random matrices are used to obtain the expressions for the higher-order cumulant and spectral vectors of a linear vector process as defined above. Then it is shown that linearity of a vector process implies constancy of the modulus square of its normalized higher-order spectra whereas the component of such a vector process does not necessarily have a linear representation. Finally, statistics for the testing of multivariate Gaussianity and linearity are proposed.     

A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing

This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.     

电路模拟中非线性方程的周期波形响应

用范数估计方法对非线性高阶微分方程的周期边值问题进行了讨论,通过对非线性二阶微分方程周期边值问题的详细讨论,给出了系统函数对某些变量偏导数的某种范数小于1时,非线性二阶微分方程的波形松弛算法产生的迭代序列收敛到该方程的周期解.用类似的方法给出了非线性高阶微分方程的波形松弛算法产生的迭代序列收敛到该方程周期解的充分性条件.