A WELL-CONDITIONED MATRIX FOR (kuX)X WITH DISCONTINUOUS k

The traditional tridiagonal matrix approximating the one-dimensional heat equation is ill-conditioned when heat conductivity changes radically. An algebraic reformulation of the tridiagonal produces a well-conditioned matrix. Additional variables are rates q=−ku_x at interfaces between radical changes in k. A reduced matrix amounts to a coarse approximation.     

THE COMPUTATION OF WAVELET-GALERKIN APPROXIMATION ON A BOUNDED INTERVAL

This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a bounded interval.     

Determination of exchange enthalpy and entropy parameters of poly(dimethyl siloxane) with some n-alkanes by inverse gas chromatography

The total interaction parameter at infinitely high polymer concentration. χ_t^∞, and the effective exchange energy parameter, X̄₁₂, of poly(dimethyl siloxane) with n-pentane, n-hexane, n-heptane and n-nonane were determined around room temperature using the inverse gas chromatography technique. The values of χ_t^∞ are in agreement with corresponding literature values. The exchange enthalpy X₁₂ and entropy, Q₁₂, parameters were determined at the same temperature. The X₁₂ parameters increase with the carbon number of the n-alkanes, while their temperature dependence is almost negligible. The Q₁₂ parameters are approximately independent of temperature and carbon number of the n-alkanes.     

A SINGLE-DOMAIN BOUNDARY ELEMENT METHOD FOR 3-D ELASTOSTATIC CRACK ANALYSIS USING CONTINUOUS ELEMENTS

A boundary element method is presented for single-domain analysis of cracked three-dimensional isotropic elastostatic solids. A numerical treatment for the hypersingular Boundary Integro-Differential Equation (BIDE) for displacement derivatives is described, in which continuous boundary elements may be used. Hadamard principal values of the hypersingular integrals arising in the formulation are evaluated using polar co-ordinates defined on the tangent planes at the source point, and the free term coefficients are calculated directly using a numerical technique. The forms of the Boundary Integral Equation (BIE) and the BIDE are considered for a source point on the coincident surfaces of a crack, and a scheme is given for defining the Traction Boundary Integral Equation TBIE so that it optimally incorporates the traction information deficient in its complementary partner, the BIE. Numerical results for some example mixed-mode crack problems are presented.     

低速冲击下短纤维复合材料本构方程研究

借助ZWT非线性粘弹性一维本构关系,导出了常应变率条件下,热固性聚合物不含时间变量和积分项的、简化的、三次多项式型本构方程;采用细观力学方法,将建立在线弹性理论之上的Eshelby等效包容体理论推广应用于非线性弹性问题.在上述工作基础之上,结合应变率影响,提出了低速冲击下随机分布短纤维复合材料的一维率相关本构方程;把方程预测结果与实验结果对比,发现吻合很好,因而初步验证了所提本构方程的可靠性.     

基于非线性小波阈值的各向异性扩散方程

本文给出了林石算子定义的扩散方程的小波阈值等价形式,并在此基础上对林石算子定义的扩散系数计算公式进行了修改,将其中估计各阶导数时所用的高斯线性滤波图像改成平移不变小波非线性阈值图像,这样避免了高斯滤波引起的过度光滑和边界移动.实验结果表明新的扩散方程在保持边缘位置的同时能更有效地去除噪声.     

Laplace方程分域展开方法

针对电磁场分析中有限元法适应能力强,但计算量大,效率低,而解析法计算量小,但适用范围窄的各自优缺点,将有限元方法与解析方法相结合,提出了一种分域展开的半解析方法用以求解工程电磁场问题。依据龙格定理,把复杂的求解场域分割为若干形状简单的子域,在每个子域内利用本征函数构造半解析展开式逼近方程的解,然后通过子域拼接得到整个场域的解。展开式系数用配点法确定。由于采用解析展开式,逼近效率高,减少了未知数个数;同时由于是局域逼近,具有解函数形式简单,计算量小,矩阵是稀疏的,条件数小,易于求解,实施方便等优点。以二维Laplace问题为研究对象,数值算例验证了方法的有效性,表明该方法花费时间短,计算精确度高。     

低渗透非达西气体渗流模型及计算方法

在一系列假定条件下,建立了一个低渗透非达西气体渗流的非线性移动边界偏微分方程数学模型,在理论上论证模型解的存在唯一性基础上,用对数网格对求解区域进行剖分,建立显式预测隐式校正格式,进而讨论模型的算法。此模型和算法具有一定的应用价值。     

基于正演模拟的地震反射特征主要影响因素分析

随着储层地球物理学的发展,利用地震信息直接预测储层砂岩厚度的横向变化,愈来愈迫切要求对地震数据进行高保真处理。利用波动方程理论法对楔形体砂岩模型进行正演模拟,探讨了随机噪声、地层吸收对地震记录、地震属性以及砂岩预测结果的影响。分析认为,当Q小于100时,地层对地震反射能量吸收严重,需要在处理中加强能量补偿。当S／N小于5时,储层砂岩厚度与地震反射特征、地震属性的相关性变差,噪声对预测结果产生干扰,影响储层预测精度。     

波动方程最优分裂步相移(OSP)偏移方法研究及应用

波动方程叠前深度偏移是复杂构造准确成像的最有效手段,它用可描述波在复杂介质中传播过程的算子来实现波场外推,更适用于复杂介质中波的成像,此外,它还具有保振幅性的优点。波动方程叠前深度偏移的核心问题就是波场外推算子,一般要求算子能适应陡倾角反射的成像和较剧烈的横向速度变化,同时还要有较高的计算效率。介绍了OSP算子的基本原理及特点,并与其他几种偏移方法进行了比较;同时用OSP方法研制的软件在大庆油田进行了实际应用,取得较好的效果,表明该方法具有良好的应用前景。