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.     

建筑制图标准中图形符号适宜性、区分性的研究

应用线段长短、间距大小视觉反应的量化规律，提出设计图形符号大小的原则——既更使其大小满足“长”“短”“大”“小”的心理要求，又要互相之间在大小上有区分性。根据图形组织的相似、接近、连续三原则提出设计图形符号形状的原则——图形符号之间尽量减少相似、接近、连续，以保证较好的区分性。通过分析发现，现行建筑制图标准中的图形符号绝大部分在大小和形状具有适宜性、区分性。     

代数曲面的几何连续过渡及其应用

本文对代数曲面的几何连续拼接作了研究，给出了多个代数曲面的几何连续过渡方法，同时给出了一种基于分片的曲面过渡方法。     

四方连续式面料图案的自动生成算法

提出了自动合成四方连续面料图案的数学模型;介绍了人机交互色彩调配算法;从数学模型、色彩处理、应用前景库三方面对有关设计思想和实现方法作了详细说明.     

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．