基于消息传递的时域分解并行算法研究

将Parareal算法中的预估校正格式加以改进,提出时域分解并行算法。基于主从模式和消息传递,具体考察了群体通信和非阻塞通信模式,并设计出通用而简便的并行化模型。在集群系统下对热传导方程和对流扩散方程的数值模拟结果表明:算法具有较高的加速性能以及良好的可扩展性,体现了时域分解的独特优势。     

分数阶非线性多智能体系统的一致性研究

研究固定拓扑结构下的分数阶非线性多智能体系统协调控制的动力学模型问题。由于实际多智能体系统中,系统的状态变量难以全部测量,为了克服这一困难,利用状态观测器对系统状态进行重构并基于重构状态进行状态反馈。利用分数阶Lyapunov稳定性理论,证明了当反馈增益矩阵满足一定的线性矩阵不等式（LMI）条件时,系统中的智能体最终趋于所给定的目标状态。最后利用分数阶微积分的预估-校正算法进行数值仿真验证了理论分析的有效性和可行性。     

改进的NURBS曲线预估校正插补方法

现行的NURBS曲线参数预估校正插补方法不能预估最开始的两个参数,而且不能控制预估参数迭代修正的次数。提出改进的NURBS预估校正插补方法,该方法预估插补点参数,根据最大进给步长约束、轮廓误差约束以及法向加速度约束,判定预估参数与实际参数的误差,当误差在允许范围内,则对参数步长增量进行调整,否则进行迭代修正。仿真实验结果表明,新方法通过对参数步长增量的调整,使得预估参数更加接近实际参数,较现有方法有效减少了参数迭代修正的次数,利于实时插补的实现。     

A robust solver using a continuation method for Nevanlinna-Pick interpolation with degree constraint

This note modifies a previous algorithm for solving a certain convex optimization problem, introduced by Byrnes, Georgiou, and Lindquist, to determine any Nevanlinna-Pick interpolant satisfying degree constraint. The modified algorithm is based on a continuation method with predictor-corrector steps and it turns out to be quite efficient and numerically robust.     

A predictor-corrector scheme for fourth order parabolic partial differential equations

A novel predictor-corrector method is developed for the numerical solution of fourth order parabolic partial differential equations (PDEs) occuring in the deflection of a Euler-Bernoulli beam hinged at both ends. The scheme is fourth order accurate in time and computationally efficient on serial or parallel machines as compared to implicit methods.     

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.     

求解常微分方程初值问题的并行块预估——校正方法

针对多处理机系统构造了一类具有较高并行度的并行块预估－校正方法。在ｋ＝２，ｓ＝３的情况下，给出了一个具有四介精度的并行计算公式，并讨论了该方法的稳定性，数值结果表明该计算公式对求解常微分方程是有效的。ｒ     

基于多线程并行强化学习的建筑节能方法

提出一种基于并行强化学习的建筑节能方法，该方法结合多线程技术和经验回放方法提出一个多线程并行强化学习算法框架，其新颖点在于：在经验回放过程中引入自模拟度量方法，通过计算样本之间的距离，选取低相似度的样本构造多样样本池，Agent的学习过程从多样样本池中选取样本学习，可有效避免浪费学习资源。实验包括在仿真房间模型上与Q-Learning算法的对比实验和与经典PID控制方法的对比实验。实验结果表明，所提出的并行算法有更快的学习速率和收敛速度，能更快地求解出最优策略，并拥有更高的运行效率。     

Explicit momentum conserving algorithms for rigid body dynamics

Two new explicit time integration algorithms are presented for solving the equations of motion of rigid body dynamics that identically preserve angular momentum in the absence of applied torques. This is achieved by expressing the equations of motion in conservation form. Both algorithms also eliminate the need for computing the angular acceleration. The first algorithm employs a one-pass predictor-corrector scheme while the second algorithm is based upon the staggered time integration approach of Park. Numerical results are presented comparing the new algorithms to the algorithms of Simo and Wong and Park et al. The predictor-corrector algorithm is shown to suffer weak instabilities while the staggered conserving algorithm exhibits improved performance compared to the staggered algorithm of Park et al.     

A low Mach number scheme based on multi-scale asymptotics

The low Mach number regime is characterized by a large discrepancy between the flow velocity and the speed of sound, leading to physical effects on different length scales and of different orders of magnitude. A single time scale, multiple space scale asymptotic analysis provides detailed insight into the limit behavior of solutions of the compressible Euler equations as the Mach number tends to zero. This analysis shows that “the pressure” splits up into three parts with different physical meanings. This knowledge is then used to develop a numerical scheme including multiple pressure variables to account for the different effects. The numerical method is a semi-implicit predictor-corrector algorithm. In the predictor step, the asymptotic equations are used to guess the global and large scale effects. Then the corrector step can be viewed as an incompressible solver with compressibility effects acting as source terms. Received: 28 July 1999 / Accepted: 21 September 1999     

Efficient parallel algorithm for statistical ion track simulations in crystalline materials

We present an efficient parallel algorithm for statistical Molecular Dynamics simulations of ion tracks in solids. The method is based on the Rare Event Enhanced Domain following Molecular Dynamics (REED-MD) algorithm, which has been successfully applied to studies of, e.g., ion implantation into crystalline semiconductor wafers. We discuss the strategies for parallelizing the method, and we settle on a host-client type polling scheme in which a multiple of asynchronous processors are continuously fed to the host, which, in turn, distributes the resulting feed-back information to the clients. This real-time feed-back consists of, e.g., cumulative damage information or statistics updates necessary for the cloning in the rare event algorithm. We finally demonstrate the algorithm for radiation effects in a nuclear oxide fuel, and we show the balanced parallel approach with high parallel efficiency in multiple processor configurations.     

一个多维次成分并行提取算法及其收敛性分析

次成分分析是信号处理领域内一项重要的分析工具.目前,多维次成分并行提取算法数量稀少,而且现有的算法在应用时还存在很多限制条件.针对上述问题,在分析研究OJAm次子空间跟踪算法的基础上,采用加权矩阵法提出了一种多维次成分提取算法,并采用递归最小二乘法对所提算法进行了简化,最后采用李雅普诺夫函数法确定了所提算法的全局收敛域.相比现有算法,所提算法对信号的特征值大小没有要求,也不需要在迭代过程中进行模值归一化操作,同时算法具有较低的计算复杂度.仿真实验表明:所提算法能够并行提取多维次成分,而且收敛速度要优于现有同类型算法.     

基于CUDA实现MRRR算法并行

MRRR(Multiple Relatively Robust Representations)算法是求解对称三对角矩阵本征值问题高效、精确的算法之一。在分析MRRR算法及CUDA(Compute Unified Device Architecture)并行体系结构的基础上,针对算法的可并行性,采用单指令多线程并行方式实现了基于CUDA的MRRR算法并行,并从存储结构方面优化算法。实验结果显示,与LAPACK库中串行MRRR实现相比,并行方法在保证精度的基础上获得了20倍的加速比,进而从计算精度和计算时间上说明MRRR算法适合在GPU上并行。     

一种面向多核系统的并行计算任务分配方法

随着多核处理器的普及,目前的大规模并行处理系统普遍采用多核处理器,这对于资源管理和调度提出了更高的要求.提出了基于共享Cache资源划分的方法,建立了面向多核处理器支持Cache资源分配的进程调度模型,设计并实现了并行任务到多核处理器的映射算法,更好地解决了大规模资源管理系统中面向多核处理器的任务分配问题,降低了使用共享Cache的多个进程运行时的相互干扰,提升了应用程序性能.     

结合面积度量和误差校正的网格简化算法

提出了一种基于边折叠的网格模型简化的新方法。考虑到模型的局部形状特征，算法将局部面积度量因素加入简化计算过程，与二次方距离误差测度一起组成新的误差目标函数。还提出了计算二次方误差矩阵的预测-校正模型，用于降低简化累积误差。实验结果表明，该算法通用性较强，能够显著提升模型的简化质量，特别是对于曲率变化剧烈的模型表面，其简化模型能够更好地保持原有特征。     

面向密码流处理器的AES算法软件流水实现方法

针对轮函数在分组密码实现过程中耗时过长的问题,提出了面向可重构密码流处理器（RCSP）的高级加密标准（AES）算法软件流水实现方法。该方法将轮函数操作划分为若干流水段,不同流水段对应不同的并行密码资源,通过并行执行多个轮函数的不同流水段,从而开发指令级并行性提高轮函数执行速度,进而提升分组密码的执行性能。在RCSP的单簇、双簇和四簇运算资源下分析了AES算法的流水线划分过程和软件流水映射方法,实验结果表明,该软件流水实现方法使得单分组或多分组不同数据分块的操作并行执行,不仅能够提升单分组串行执行性能,还能够通过开发分组间的并行性来提高多分组并行执行性能。     

A New Robust Algorithm to Trace Curves

We are presenting here a new reliable algorithm to trace curves using interval arithmetic. We give several computable criteria which guarantee the convergence of the correction step of the classical predictor-corrector method. Our method avoids, for instance, to jump from a component of the curve to another one; this kind of mistake typically causes inconsistencies in the topology of intersecting surfaces in geometric modelers.     

A parallel processing algorithm for nonlinear programming problems

Algorithms for solving multiple criteria nonlinear programming problems are frequently based on the use of the generalized reduced gradient (GRG) metod. Since the GRG method gives complex and large size processing for computation, it takes much time to solve large-scale multiple criteria nonlinear programming problems. Therefore, parallel processing dealing with the GRG method is required to solve the problems. We propose a parallel processing algorithm for the GRG method under multiple processors systems.     

基于多链拓展编码方案的量子遗传算法

为了提高量子遗传算法的性能,提出了一种基于多链拓展编码方案的量子遗传算法。根据编码方案,将每个量子位分解为多个并列的基因,有效地拓展了搜索空间;结合编码方案提出量子更新策略,并引入了动态调整旋转角机制对个体进行更新,使用量子非门变异策略实现量子变异。仿真实验中,分析了使用不同变异概率[0,0.1,…,0.9,1]时对算法性能的影响,对比了分别使用普通量子遗传算法、双链编码方案、三链编码方案以及四链编码方案的量子遗传算法在优化函数极值问题时算法的性能。实验结果证明,通过增加基因链可以显著提高算法的性能,多链拓展编码方案可以提高量子遗传算法的性能,是有效的。     

应用并行进化策略求解柔性调度问题

该文研究应用多种群并行进化策略(MPES)求解FMS中的柔性调度问题。仿真结果表明,该算法能增强进化算法的全局收敛性,在多目标和复杂的多约束条件下,能得到满意的全局最优解。