外推瀑布多网格法(EXCMG)——-大规模求解椭圆问题的新算法

基于有限元的渐近展开式,导出了新的外推公式,它们更精确地逼近密网上的有限元解(而不是微分方程的解).提出了新的外推瀑布型多网格法(EXCMG),采用新外推公式及其二次插值提供密网上的好初值.数值实验表明,新方法有很高的精度和效率.最后在PC机上求解了大规模二维椭圆问题.     

制约并行算法的执行效率分析

本文用随机变量矩阵描述相互制约并行算法中各子计算之间的相互关系,分析了在并行处理系统上的执行效率。在特殊规则下,求得了并行算法期望执行效率的一般表达式,以及随算法结构的“特征矩阵的连续变化”,算法的期望执行效率增减的判定定理。     

战时备件配送的MDVRPTW问题研究

战时备件配送的车辆调度是提高装备保障效率的关键因素.以装备效能损失最小化为车辆调度的目标,建立了问题的M DVRPTW模型,并应用蚁群算法对问题进行了求解.算法中,根据问题特征改进了状态转移规则,设计了串行和并行两种路线构造方法,并应用局部搜索模块对蚂蚁构造的路线进行改进.对算例的计算实验表明,串行路线构造方法在精度和速度两方面均优于并行路线构造方法.     

基于SFA与DEA模型的创新型城市科技创新效率实证研究

分别运用SFA模型和DEA模型对10个样本城市2001-2010年的科技创新效率进行定量测度,并对两种方法测度出的创新型城市科技创新效率值排序进行相关分析和一致性检验.结果表明两种方法测度出的创新型城市科技创新效率在数值上有显著差异,但在效率排序上具有很好的一致性.     

由吴方法计算零维系统的有理单元表示

本文提出一个计算零维系统的有理单元表示的新算法.无需进行Grbner基运算,我们的算法仅运用了著名的吴方法.基于吴方法,我们的算法在Maple平台上被编制成一个通用程序RUR-Wu,可快速地计算出零维系统的有理单元表示.作为一个应用,本文提出了一个有效方法,用来计算某些多项式的整体最小值.此外,本文给出了几个实例,用来表明算法的效率.     

左截断相依数据下条件分位数的双核局部线性估计

本文在左截断相依数据下,利用局部线性估计的方法,先提出了条件分布函数的双核估计;然后利用该估计导出了条件分位数的双核局部线性估计,并建立了这些估计的渐近正态性结果;最后,通过模拟显示该估计在偏移和边界点调节上要比一般的核估计更好.     

考虑环境因素的中国城市经济效率评价研究

在考虑环境因素情形下,实证考察中国城市经济效率水平.引入环境因素,构建中国城市经济效率评价指标体系;运用DEA-BCC模型对中国31个省会城市和计划单列市的经济效率进行评价,计算得出各决策单元的DEA评价值,并进行效率分析、投入冗余产出不足分析和区域比较分析.考虑环境因素情形下,中国城市经济效率总体上较好,综合效率、纯技术效率和规模效率平均值分别达0.912、0.855和0.940,但个体差异较大,存在个体间的非均衡发展;从规模报酬来看,太原、福州、南昌等10个决策单元的经济规模应适当增加;长春、哈尔滨、南京等9个决策单元的经济规模应适当减少;太原、长春、哈尔滨等16个决策单元存在不同程度的投入冗余和产出不足,亟待改进;中国城市经济效率存在区域间的非均衡发展,综合效率平均值呈现东部地区最高,中部地区次之,西部地区最低的格局.     

删失指标随机缺失下一类非参数函数的加权局部多项式估计及其应用

本文在右删失数据中删失指标部分随机缺失下,构造了一类非参数函数的校准加权局部多项式估计以及插值加权局部多项式估计,并建立了这些估计的渐近正态性;作为该方法的应用,导出了条件分布函数、条件密度函数以及条件分位数的加权局部线性双核估计和插值加权局部线性双核估计,并且得到了这些估计的渐近正态性;最后,在有限样本下对这些估计进行了模拟.     

基于DEA模型的地区经济发展差异评价——以肇庆市为例

利用数据包络技术对肇庆市2006年10个经济区域的技术效率和规模效率进行研究,计算了肇庆市10个经济区域经济发展的相对效率值,从有效性的角度分析肇庆市中心城区、东南板块、山区板块的发展状况,并对产生效率差距的原因和改进方向进行了探讨.     

三维有限元法中等参数六面体单元的单元分析

我们用有限单元法,在6912机上编制了三维等参数六面体混合单元通用程序。经过几年来,清华大学水利系,水电部第四、第八、第十三等工程局,铁道部大桥局、煤炭部河北煤矿设计院等二十多个单位对不同的工程实际问题,用此程序进行计算,都取得了较满意的成果。为便于交流和使用本程序的同志对程序有所了解,现将本程序所采     

L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

Extrapolation cascadic multigrid method on piecewise uniform grid

The triangular linear fnite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed.Global superconvergence in discrete H1-norm and global extrapolation in discrete L2-norm are proved.Based on these global estimates the conjugate gradient method(CG)is efective,which is applied to extrapolation cascadic multigrid method(EXCMG).The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.     

Analysis of extrapolation cascadic multigrid method(EXCMG)

Based on an asymptotic expansion of finite element,a new extrapolation formula and extrapolation cascadic multigrid method(EXCMG)are proposed,in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid.In the case of triple grids,the error of the new initial value is analyzed in detail.A larger scale computation is completed in PC.     

TIME-EXTRAPOLATION ALGORITHM （TEA） FOR LINEAR PARABOLIC PROBLEMS

The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.     

The nonequispaced FFT on graphics processing units

Without doubt, the fast Fourier transform (FFT) belongs to the algorithms with large impact on science and engineering. By appropriate approximations, this scheme has been generalized for arbitrary spatial sampling points. This so called nonequispaced FFT is the core of the sequential NFFT3 library and we discuss its computational costs in detail. On the other hand, programmable graphics processing units have evolved into highly parallel, multithreaded, manycore processors with enormous computational capacity and very high memory bandwidth. By means of the so called Compute Unified Device Architecture (CUDA), we parallelized the nonequispaced FFT using the CUDA FFT library and a dedicated parallelization of the approximation scheme. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

指数分布族中矩估计序贯置信区间

在矩估计的基础上,对于给定精度(2d)及置信系数(α),建立了对参数函数g(θ) 的一个序贯置信区间估计的程序．并讨论了在一定条件下,当d→0,它的渐近相合性、渐近有效性及有界的最优费用差(EN(d)-n(d))等渐近性质．     

Two-step peer methods with continuous output

The essential feature of peer methods for initial value problems is that all stages have the same order. Hence, dense output is easily available by interpolation. However, continuity of the output requires that the methods possess the FSAL-property (first same as last) well known from one-step methods. An additional advantage of such methods is an increase of the number of stages and the order without increasing the computational effort of the scheme or the number of computing cores for parallel methods. We derive several FSAL peer methods with 3 to 9 stages and compare their numerical efficiency with existing methods in the case of explicit parallel and implicit sequential peer methods.     

A GPU based iteration approach to efficiently evaluate radiation symmetry for laser driven inertial confinement fusion

Radiation computation is very important for high energy density experiments design in the laser-driven Inertial Confinement Fusion. The view-factor based models are often used to calculate the radiation on the capsule inside a hohlraum. However, it usually takes much time to solve them when the number of equations is very large.In this paper, an efficient iteration approach GPU is presented. The core idea is: (1) guaranteed symmetry, strictly diagonally dominant, and positive definite properties underlying the models are described, (2) a preconditioned conjugate gradient iteration approach is presented to compute the radiation based on such guaranteed properties, and (3) such approach is then parallelized and implemented for GPU so that the large scale models, especially for the non-linear model, can be efficiently solved in reasonable time.Finally, two experimental targets for Shenguang laser facilities built in China are demonstrated and compared to validate the efficiency of the presented approach. The results show that, the models’ computation (1) can be speeded up with successive over-relax iteration method by eight times as compared with Cholesky factorization based direct approach, (2) can be accelerated more with the preconditioned conjugate gradient iteration approach by almost eight times, and (3) can be further accelerated about 2 to 4 times as it parallelized and run on the GPU, which enables the large scale models, can be efficiently solved in reasonable time on the usual desktop computers.     

Effective optimization-based approach for designing active noise control systems in enclosures

An efficient constrained optimization-based prototype program OPTANC is developed to expedite the optimum design of active noise control systems in enclosures. The boundary element method is used to model the sound field of enclosures in which the walls provide complex impedance and point noise sources may exist at arbitrary locations. A sequential quadratic programming algorithm is selected as the optimizer for the deisgn because of its accuracy, efficiency, and reliability. The program is coded in C with portability on micro, mini, and mainframe computers, and is also modularized for future expansion. Simulations show that the software can effectively and efficiently produce the optimal locations and sound strengths of the control sources for active noise control problems.