含两个参数的奇异摄动问题的差分进化算法

针对在Shishkin网格上数值求解含有两个参数的奇异摄动问题,在有限差分方法的基础上,将Shishkin网格过渡点参数选取问题转化成一个无约束优化问题,并采用差分进化算法进行求解。数值结果表明用差分进化算法得到最优Shishkin网格参数后,奇异摄动问题的数值解在边界层的精度得到了明显的提高,进一步说明了方法的有效性和可靠性。     

中尺度数值气象预报模式MM5并行性能分析与优化

气象预报模型的准确度与实时性是防震减灾工作的关键支持。MM5是成熟的并行化的中尺度数值气象预报模型。本文在阐述MM5并行模式及并行实现的基础上，具体分析了MM5在IBM eServerp Series 690主机上并行性能，并给出相应的优化方案。     

PEBI网格节点编号优化方法研究

基于PEBI网格的油藏数值模拟能够更准确地模拟地下油藏流动,模拟过程中主要是求解以PEBI网格为差分单元的有限差分方程。提出采用谱算法优化PEBI网格节点的编号来减少差分方程中系数矩阵的带宽,以节约计算时间和数据存储量。首先计算网格按初始编号所形成的邻接矩阵及其Laplacian矩阵,然后通过计算Laplacian矩阵的特征值和特征向量得到Fiedler特征向量,最后对Fiedler特征向量进行排序,并根据排序后的向量对PEBI重新编号。最后通过实验验证了谱算法在PEBI网格编号优化中的有效应用。     

气象计算网格模式预报系统的建立与优化*

为了在气象部门内跨地域共享使用MM5模式系统,基于建成的气象计算网格平台,成功地接入了MM5模式系统。根据用户预报需求,设计了参数化和业务运行方案,建立了华中区域MM5数值预报应用系统。完成模式系统部署运行后,通过使用网格平台的资源调度和工作流引擎等工具手段,优化了后处理运行流程。运行分析表明网格平台上MM5模式系统的运行效率显著提高。     

气象应用基准测试程序MM5 Benchmark并行性能优化

由美国国家大气研究中心(NCAR)和宾夕法尼亚大学(PSU)共同开发的MM5模式是目前气象领域广泛采用的中尺度模式之一。由于MM5模式的广泛应用和计算特点,MM5 Benchmark成为了高性能计算领域衡量计算机实用性能的典型应用之一。本文介绍了MM5模式的并行计算方法,针对目前流行的Intel Itanium-2 CPU特点,在性能分析的基础上,从编译选项、代码优化、区域分解、处理机拓扑结构等方面对程序性能进行优化。实际测试结果表明,在某国产巨型机上优化后的持续计算性能最大提高20%左右。     

奇异摄动反应扩散方程数值模拟的粒子群优化算法

针对Shishkin网格方法在数值求解奇异摄动反应扩散方程时,网格过度点参数的选取具有不确定性的缺陷,提出了一种用粒子群优化(PSO)算法估计Shishkin网格参数的方法。首先基于有限差分方法,构造了以误差范数最小为目标的无约束优化问题,并用PSO算法进行了求解。该方法克服了人为选择参数的缺陷。实验结果表明：与单纯形算法相比,PSO算法在优化Shishkin网格参数时能够收敛到全局最优解;而且在最优网格参数下,奇异摄动反应扩散方程的数值结果在边界层的精度也得到了明显提高,进一步说明了所提方法的有效性和可行性。     

气象系统初探巴塞罗那真四核威力

气象预测一直是高性能计算机产品的主要用户之一，其为人民提供日常生产、生活所必须的信息资料。作为国内服务器行业领军企业的曙光公司。在气象行业应用中有着广泛的经验，早在2002年，曙光公司就推出了基于MM5模式的气象专用机，充分优化了并行机上的MM5模式。随后，曙光公司在2004年为气象行业完成了从32位平台到64位平台的移植。[第一段]     

基于差分隐私的轨迹模式挖掘算法

针对现有基于差分隐私的频繁轨迹模式挖掘算法全局敏感度过高、挖掘结果可用性较低的问题,提出一种基于前缀序列格和轨迹截断的差分隐私下频繁轨迹模式挖掘算法--LTPM。该算法首先利用自适应的方法获得最优截断长度,然后采用一种动态规划的策略对原始数据库进行截断处理,在此基础上,利用等价关系构建前缀序列格,并挖掘频繁轨迹模式。理论分析表明LTPM算法满足ε-差分隐私;实验结果表明,LTPM算法的准确率（TPR）和平均相对误差（ARE）明显优于N-gram和Prefix算法,能有效提高挖掘结果的可用性。     

大攻角叶栅绕流的高效算法

51．引言数值模拟大攻角叶栅绕流中叶片表面的分离和激波一般需要较密的计算网格，这增强了问题的刚性，过长的计算时间还会使误差积累从而导致计算失败．复杂流动数值模拟的关键之一应是尽量减少计算格点数目和计算量．差分方法中有两类基本格式，一类基于中心差分，另一类是迎风类格式，如矢通量分裂法（FVS）和通量差分分裂法（FDS）．比较研究表明山；用于边界层计算时FVS比中心差分类方法稍差，但FDS，如基于Roe近似Riemann解的格式，就比中心差分方法好，而且所需网格点要少1／2NI／4‘可见，对同时含有激波和分离的粘性流动，…     

时域有限差分算法的FPGA加速技术研究

针对各种嵌入式应用中对实时电磁场计算的需求,提出了一种新的时域有限差分法的硬件方法,采用FPGA作为硬件加速部件,加速电磁场时域有限差分算法(FDTD)的计算.采用滤波器技术重新改写时域有限差分法,将时域有限差分法的求解变成对应的硬件滤波器的设计问题,通过设计合适的滤波器完成时域有限差分的计算.实验结果表明,与时域有限差分算法的软件执行相比,硬件实现可以获得5倍左右的性能加速,能够充分发挥FPGA的计算性能.本研究能够进一步扩展时域有限差分算法的应用领域,尤其是扩展到以前因为计算性能无法应用的领域.     

基于时域有限差分和非参数核回归的室内移动通信干扰信号预测模型研究

针对网络优化和干扰实施中电磁辐射预测准确率不高的问题,本文利用多制式移动通信干扰器对室内的复杂场景进行了干扰防护的信号强度预测,对实际场景建立几何模型后采用时域有限差分算法获得信号强度预测值,并结合实际测量改进非参数核回归预测算法获得统计分析预测值,最后提出混合加权预测模型,对电磁辐射进行定量预测分析。预测结果表明,本文提出的基于时域有限差分算法和非参数核回归算法的混合加权预测模型能对复杂室内场景下信号强度进行预测,准确率较高。     

Finite-difference schemes for the computation of viscoplastic medium flows in a channel

Two finite-difference schemes for the computation of incompressible Bingham fluid flows in pipes are proposed. The variational Duvaut-Lions inequality is used as a mathematical model. One of the difference schemes is an analogue of the well-known MAC (marker-and-cell) scheme on staggered grids, the second employs one grid for velocity approximation, and the other for all the components of the strain rate tensor. The convergence of finite-difference schemes and the iteration method are studied. The obtained results are compared with those known from publications. The proposed schemes were used to compute Bingham medium with an inhomogeneous yield stress.     

高密度电阻率法在煤矿岩溶探测中的应用研究

文章详细介绍了高密度电阻率法的工作原理和电阻率三维有限差分的数值模拟方法。针对矿井下可能存在的岩溶特征建立了一个具体的岩溶数学模型,并通过正演模拟合成了反射剖面图。计算结果表明,利用高密度电阻率法三维有限差分正演模拟煤矿岩溶,完全可以得到岩溶的特征信息,为进一步治理矿井隐藏岩溶提供了依据。     

The importance of boundary conditions in the simulation of dissolution in the USP dissolution apparatus

As shown in previous papers, mathematical simulation can be useful in the design of drug delivery systems. We present a finite-difference approximation to the drug mass transfer rate from dissolving cylindrical drug-containing compacts, consisting of alternating layers of drug and inert material. Results are compared with a recent analytical solution to the same problem and with experiment. The two theoretical estimates differ by about 10%, a result of different implementations of a derivative surface boundary condition. The finite-difference model is more physically realistic but the analytical solution is usefully accurate.     

A second-order explicit scheme for the numerical solution of a fox-rabies model

A second-order, unconditionally-stable, finite-difference scheme is developed for the numerical solution of the SI model of fox-rabies dynamics. The local stability of the scheme, by direct inspection of the eigenvalues dependent on the time step size and on two parameters, is shown to be unconditionally stable.     

一种强跟踪有限差分滤波二元估计算法

针对非线性工业过程测量的滞后性和模型不确定性给系统状态估计和模型参数估计造成的困难,在扩展Kalman滤波器（EKF）的基础上,引入有限差分滤波器（FDEKF）和次优渐消因子,提出了一种强跟踪有限差分滤波状态和参数二元估计算法。该二元估计算法将滤波器分解为参数滤波和状态滤波两个过程,分别估计模型参数和系统状态。最后,将该算法应用于一化学反应过程的仿真,结果表明,这种强跟踪有限差分滤波的二元估计算法在原模型或参数存在偏差的情况下,仍能较准确地估计系统状态和模型参数,并具有较强的数值鲁棒性。     

Numerical methods for nonlinear integro-parabolic equations of fredholm type

This paper is concerned with iterative methods for numerical solutions of a class of nonlocal reaction-diffusion-convection equations under either linear or nonlinear boundary conditions. The discrete approximation of the problem is based on the finite-difference method, and the computation of the finite-difference solution is by the method of upper and lower solutions. Three types of quasi-monotone reaction functions are considered and for each type, a monotone iterative scheme is obtained. Each of these iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite-difference system. This monotone convergence leads to an existence-uniqueness theorem as well as a computational algorithm for the computation of the solution. An error estimate between the computed approximations and the true finite-difference solution is obtained for each iterative scheme. These error estimates are given in terms of the strength of the reaction function and the effect of diffusion-convection, and are independent of the true solution. Applications are given to three model problems to illustrate some basic techniques for the construction of upper and lower solutions and the implementation of the computational algorithm.     

Numerical Solution of a Flow Equation of the Ideal Liquid whose Vorticity Is Proportional to the Flow Function

The paper deals with the solution of an equation that describes a particular case of the flow of the ideal liquid in which the vorticity is proportional to the flow function. To solve the equation, two methods are used, namely, the finite-difference method and a method based on the Hermite formula. The results of solution of model problems by both methods are presented and compared.     

The 2F3D-Model of Filtration in the Bottom Zones of Horizontal Oil Wells. II

The difference approximation in time and space of the original continuous equations (Part I) was discussed. The existence conditions for the corresponding algebraic equations were presented. The solution of the difference equations was proved to converge to that of the original equations of the continuous model. The problem of identification of the basic parameters of the finite-difference model was discussed.     

基于MATLAB的FDTD两种常见吸收边界条件的编程

本文介绍了时域有限差分法的基本原理。结合两种常见的吸收边界条件，以具体模型为例，阐述了基于MATLAB编程的基本流程，并给出了用MATLAB绘制的场图。