一种求解非线性无约束优化问题的充分下降的共轭梯度法

共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能.     

大规模边界元模态分析的高效数值方法

随着大规模快速边界元计算技术的发展,在复杂结构的动态设计、振动与噪声分析中愈来愈多地采用边界元法,因此求解大规模边界元特征值问题、进行复杂结构和声场模态分析,成为工程应用中一个十分重要,但却极具挑战性的课题,目前国际上还没有十分有效的数值方法.本文针对边界元法中典型的非线性特征值问题,提出了一种通用、高效的数值解法,称为基于预解矩阵采样的Rayleigh-Ritz投影法,记为RSRR.首先,通过求解一系列频域边界元问题来构造特征向量搜索空间,进而可以采用Rayleigh-Ritz投影,将原问题转化为一个可以采用现有方法求解的小规模缩减特征值问题;其次,为了降低Rayleigh-Ritz投影过程的计算量,基于解析函数的Cauchy积分公式,构造了边界元系数矩阵的插值近似方法,以及缩减特征值问题系数矩阵的快速计算方法,给出了插值项数的估计策略;最后,将RSRR与声学快速边界元法结合,应用于大规模吸声结构的复模态分析.数值算例表明,RSRR方法能够可靠地求出给定频段内的全部特征值和特征向量,具有计算效率高、精度高、通用等优点.     

低渗透煤层气藏中气-水两相不稳定渗流动态分析

针对低渗透煤层渗流问题,考虑启动压力梯度及其引起的动边界和动边界内吸附气解吸作用的渗流模型研究目前仅限于单相流,而更符合实际的气-水两相渗流动边界模型未见报道.本文综合考虑了煤层吸附气的解吸作用、气-水两相渗流、非达西渗流、地层应力敏感等影响因素,进行了低渗透煤层的气-水两相渗流模型研究.采用了试井技术中的"分相处理"方法,修正了两相渗流的综合压缩系数和流度,并基于含气饱和度呈线性递减分布的假设,建立了煤层气藏的气-水两相渗流耦合模型.该数学模型不仅可以描述由于低渗透煤层中渗流存在启动压力梯度而产生的可表征煤层有效动用范围随时间变化的移动边界,还可以描述煤层有效动用范围内吸附气的解吸现象以及吸附气解吸作用所引起的煤层含气饱和度的上升;为了提高模型精度,控制方程还保留了二次压力梯度项.采用了稳定的全隐式有限差分方法进行了模型的数值求解,并验证了数值计算方法的正确性,获得了模型关于瞬时井底压力与压力导数响应的双对数特征曲线,由此分析了各渗流参数的敏感性影响.本文研究结果可为低渗透煤层气藏开发的气-水两相流试井技术提供渗流力学的理论基础.     

A Modified Weak Galerkin Finite Element Method for Sobolev Equation

For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete $H^1$ and $L^2$ norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results.     

用于光谱解混的正交向量投影算法

光谱解混是高光谱技术中的关键部分,对地物成分的定量分析至关重要。线性光谱解混方法在计算端元丰度时,大多需要涉及矩阵求逆或方阵行列式的计算,导致软件实现的计算复杂度高,且硬件实现困难。同时,当端元数量增加时,算法的计算量也会随之呈指数级快速增长。论文基于传统的正交子空间投影方法,利用正交原理,提出了一种新的光谱解混方法——正交向量投影。该方法首先利用Gram-Schmidt过程计算每个端元的最终正交向量分量,并将其作为代表端元的投影向量。然后对于任意的待解混光谱向量,直接将其投影到该正交向量上。最后,计算得到投影分量的长度与正交向量的长度比,即为该正交向量所代表端元的无约束丰度。该过程避免了正交子空间投影和最小方差方法中计算复杂、实现困难的矩阵求逆运算,更便于并行计算的设计和硬件实现。通过理论的推导分析,证明了该算法与正交子空间投影和最小方差方法是完全一致的。另外,由于算法避免了矩阵相乘和求逆运算,简化了解混过程,通过对不同算法复杂度的具体分析,也证明该算法相对其他算法可以对端元数量降低一个量级。最后,在模拟数据和实际图像上分别进行实验测试,结果的分析和比较,也说明了算法的有效性。     

基于概率加权共轭梯度算法的混凝土超声波层析成像

在混凝土层析成像中,为了提高反演的准确性和计算效率,针对共轭梯度算法提出一种加权算法——概率加权共轭梯度算法.新算法不同于常规的加权算法,权重是加在成像单元上而不是方程上.为取得较好的权重因子和较好的迭代初始值,采用IART算法的权重和迭代初始值的选取方法.模拟算例和混凝土试验均表明这种加权算法的可行性.     

基于倍频移相的梯度放大器控制技术

提出了一种基于倍频移相的梯度放大器控制技术,该系统利用PLL 形成相位差通过IGBT 全桥拓扑结构以及输出功率电感并联电流输出．通过输出端闭合反馈系统和各个桥臂的均流控制反馈,实现大功率、低纹波、低噪声的电流输出．将该控制方法用于自主研制开发的梯度放大器上进行实验验证,测试得到的电流精度、纹波、噪声均达到指标要求,结果证明该设计方案具有可行性．     

A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation

In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational approach. Two additional kinds of parameters, the higher-order nonlocal parameters and the nonlocal gradient length coefficients are introduced to account for the size-dependent characteristics of nonlocal gradient materials at nanoscale. To illustrate its application values, the theory is applied for wave propagation in a nonlocal strain gradient system and the new dispersion relations derived are presented through examples for wave propagating in Euler–Bernoulli and Timoshenko nanobeams. The numerical results based on the new nonlocal strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical nonlocal stress model and the contemporary strain gradient theory. Thus, this higher-order nonlocal strain gradient model provides an explanation to some observations in the classical and nonlocal stress theories as well as the strain gradient theory in these aspects.     

Mathematical modelling of complex heat transfer in a rectangular enclosure

Numerical simulation of convective-radiative heat transfer in an enclosure with a heat source in the presence of heat-conducting walls of the finite thickness was carried out. The distributions of both local (streamlines, temperature fields) and integral (mean Nusselt numbers at typical interfaces) characteristics describing specific features of the investigated process in a real range of the variation of determining parameters were obtained. The radiation influence scales at thermal modes formation were determined. The effect of transient factor on the fields development of both hydrodynamic and thermodynamic characteristics was analysed. Correlation ratios for determining the mean Nusselt number at solid-gas interfaces were obtained depending on the Grashof number. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 08-08-00402-a).     

Recent progress on RF superconducting cavities

RF superconducting (SRF) cavities can work in continuous wave mode or long pulse mode.SRF technology has been developing rapidly since the end of the last century.RF superconducting technology is widely used in particle accelerators around the world.As the key elements, research on superconducting cavities is carried out worldwide.Besides Europe, the United States and Japan, many countries have already started SRF projects, such as Canada, India, Korea, etc.Great improvements on SRF technology have been made in China in recent years.Progress in SRF cavities is introduced in this paper.