有限元结构分析在MIMD计算机上的并行直接解法

§1.前言 并行计算是近十几年来随着并行计算机发展而发展起来的一门新兴学科,特别是对于多指令流多数据流(MIMD)的并行计算机,由于它是由多台普通计算机甚至是向量计算机相互以一定方式联结起来的新型计算机系统,因此无论是它的运算速度或存贮空     

并行求解初边值问题的有限差分方法研究

一近二十年间,随着各类并行处理机和向量计算机的问世。出现了对数值分析方法的一种新的分类法:串行算法和并行算法。在传统的串行计算机上使用的算法称为串行算法;适合于在并行计算机或向量计算机上使用的算法称为并行算法。目前由于有愈来愈多的并行机投入使用,并行算法的研究在国内外受到了普遍重视。本文概述适合于并行计算的求解扩散方程的有限差分方法研究的部分情况,其中包括作者的近期工作,希望能作为引玉之砖,引起大家的兴趣和关心。我们研究如下扩散方程的有限差分方法。     

并行迭代算法的有效性的度量参数

1．引言对于理想化的并行计算机模型山,一个并行算法的加速定义为初二万／几一地小,效率定义为Ea二Sa／a二万／（aTa）二Va／（aVI）,其中a为并行计算机的等效处理机数目,乃为已知最快的串行算法在单处理机上的运行时间,凡是所讨论的并行算法使用。个处理机的运行时间,VI为单个处理机求解问题的运算速度,而Va为0个处理机求解问题的运算速度．曼尼和几分别反映了算法并行性对计算时间改进的程度以及并行计算机处理能力发挥的程度,因此,它们是度量并行算法的有效性的重要参数．另外两个与之相人的重要参数分别为冗余度尼二几周l…     

外推瀑布式多网格法的OpenMP并行化

基于外推瀑布式多网格法(EXCMG)程序的性能分析, 采用共享存储编程标准OpenMP对EXCMG法的Fortran程序进行了并行处理,极大地提高了原串行程序的计算效率.在双核PC机和机群的一个八核SMP节点上分别进行了数值试验.结果表明: 在不改变串行程序结构的前提下, 仅对EXCMG程序中最耗时的三个子程序并行处理, 双核下并行效率可高达90%;八核下两分钟内可求解上亿个未知数的椭圆边值问题, 精度达到10^-10.     

并行列扫描Gram—Schmidt正交化方法

Gram-Schmidt正交化方法在求解线性代数方程组、最小二乘问题、代数特征值问题等很多矩阵计算问题中有着广泛的应用。因而,设计一种能在并行计算机上高效运行的GS正交化方法,必将对其他若干实际计算问题带来莫大的益处。张丽君教授在文献[2]和[3]中就方阵的正交三角分解问题作了详细的讨论。但实际情况中常遇到长方阵的正交化问题(如最小二乘问题)。本文提出一种适于并行计算的GS正交化方法,该方法采用了类似于求解三角形方程组的“列扫描”处理技巧。本算法特别适用于最小二乘等问题中常见的向量序列短而向量维数高(即后文的m(?)n)的情形,程序实现也很简单,尤其在备有内积功能部件的向量机上运行效率可达O(1)。     

关于多重网格并行计算中拟边界Jacobi成份的影响

1．引言分布式存储并行计算环境中,高效率的获取一般通过区域分解或数据分割实现大粒度并行[4]．因此,对于有效求解偏微分方程的多重网格算法[1,6],并行计算均采用网格划分进行任务分配[5],实现大粒度并行．其中,松弛算子并行度是影响算法并行效率的关键因素．Gauss－SeidellGS）点或块松弛、ILU松弛和适合于方程组的分布式GS松弛（DGS）[1,6]为多重网格算法的有效松弛算子,但本质上都是串行的．尽管采用红黑（RB）序可增强并行度,但每次松弛在每层网格上仍需两次数据交换门（即所有子网格相互交换拟边界数据）．为了减少通…     

任意长—维DFT的MIMD并行算法

本文提出了共享与分布式存储计算机上任意长—维ＤＦＴ的ＭＩＭＤ并行算法，若Ｎ＝Ｏ（ｐ，ｑ），则算法需要次算术运算。其中，Ｐ与Ｎ可为任意自然数，分别表示处理机台数与ＤＦＴ长度．本文算法具有很高的并行效率．     

适合于分布式并行计算的一种并行广义乘积型双共轭残差方法(英文)

针对求解大型稀疏非对称线性方程组,提出适合于分布式并行环境的一种并行广义乘积型双共轭残差(GPBiCR)方法(简记为PGPBiCR方法).通过重构GPBiCR方法,新方法将原方法中的三个全局同步点降低到了一个,且内积所需的通讯时间可与向量校正的计算时间有效地重叠.代价仅是稍微增加了一些计算量,而相比于全局通讯时间的降低,这是可以忽略不计的.性能和等效率分析表明,PGPBiCR方法比GPBiCR方法具有更好的并行性和可扩展性,其中可扩展性可改进3倍,而并行通讯性能可改进66.7%.数值试验得到了与理论分析相吻合的结果.     

改进伪并行遗传算法求解作业车间调度问题

针对遗传算法在求解极复杂优化问题中出现的过早收敛、执行效率差的缺点,提出了一种改进的伪并行遗传算法.该算法将并行进化与串行搜索相结合,提高了算法的收敛速度.同时该算法通过种群因子控制伪并行算法中的各子种群的规模,不仅保证了搜索过程中勘探和开采的平衡,克服过早收敛,而且减少了计算的复杂性,特别是在处理复杂优化问题上具有较高的性能.实验结果证明了该算法的有效性.     

非线性抛物组具并行本性的一般差分格式

利用具并行本性的差分方法研究非线性抛物组的边值问题。对具并行本性的一般有限差分格式证明了离散向量解的存在性、收敛性和稳定性。     

陀螺特征值问题的并行子空间迭代法

<正>1引言陀螺系统特征值问题是转子动力学中的基本问题,是一类特殊的二次特征值问题.假设M和K是n阶对称矩阵,C是n阶反对称矩阵,则二次特征值问题(λ~2M+λC+K)x=0(1)     

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

This paper deals with ultrasound medical image processing, particularly to filter the noise while preserving the edges and structures of information. The mathematical processing consists in solving by a numerical way a nonlinear evolutive boundary value problem. Several numerical semi-implicit time marching schemes are considered and analyzed. At each time step, parallel synchronous or asynchronous Schwarz alternating methods are used to solve the linear system and its convergence is studied. Lastly, the results of sequential and parallel simulations are presented.      

A parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem

In this paper, based on a two-grid method and a recent local and parallel finite element method, a parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem is proposed and analyzed. This method ensures that all the local subproblems on the fine grid can be solved in parallel. Optimal error bounds of the approximate solution are obtained. Finally, numerical experiments are presented to demonstrate the accuracy and effectiveness of the proposed method.     

On the numerical solution of integral equations with piecewise continuous displacement kernels

Solution of a Fredholm integral equation with a piecewise continuous displacement kernel is considered. It is shown that this problem is equivalent to the solution of an initial value problem for an unusual partial differential equation for continuous functions of two variables. The difference scheme for the numerical solution of the initial value problem is derived. This scheme allows implementation on parallel processors and is of linear complexity. The approach based on the numerical solution of the initial value problem is compared with a corresponding quadrature method and demonstrates certain advantages.This work was supported by the NSF grant DMS-8801961This work was supported by a research grant from the NSERC of Canada     

滩海地区运移聚集的精细数值模拟和分析

对滩海地区三层油资源运移聚集进行高精度精细平行数值模拟,提出数学模型和精细平行算子分裂隐式迭代格式,设计了并行计算程序,提出了并行计算的信息传递和交替方向网格剖分方法. 并对不同的CPU组合进行并行计算和分析,对滩海地区数值模拟结果和实际情况吻合.对模型问题进行数值分析,得到最佳阶误差估计,成功地解决了这一困难问题．     

不可压缩流动的并行数值方法

不可压缩流动的数值模拟是计算流体力学的重要组成部分. 基于有限元离散方法, 本文设计了不可压缩Navier-Stokes (N-S)方程支配流的若干并行数值算法. 这些并行算法可归为两大类: 一类是基于两重网格离散方法, 首先在粗网格上求解非线性的N-S方程, 然后在细网格的子区域上并行求解线性化的残差方程, 以校正粗网格的解; 另一类是基于新型完全重叠型区域分解技巧, 每台处理器用一局部加密的全局多尺度网格计算所负责子区域的局部有限元解. 这些并行算法实现简单, 通信需求少, 具有良好的并行性能, 能获得与标准有限元方法相同收敛阶的有限元解. 理论分析和数值试验验证了并行算法的高效性     

The Motion of a Viscous Fluid Past an Impulsively Started Semi-infinite Flat Plate

It is shown that by employing a suitable numerical method, theproblem of determining the motion of a viscous fluid past asemi-infinite flat plate which is started impulsively from restwith constant velocity parallel to itself can be solved in termsof similarity variables. The numerical solution is comparedwith previous numerical and theoretical work on the problem.The final decay to the steady-state solution described by theBlasius velocity profile is exponential in character and isfound to be substantially in agreement with theoretical predictions.     

Method for parallel construction of a committee of decision tree for processing the electroencephalography signals

A method for parallel construction of a classifier ensemble for solving the problem of localization of neuron sources within the brain on the basis of the analysis of electroencephalography signals is described. The idea of the proposed parallel numerical method consists in the consideration of the source parameters as attributes of decision tress constructed in parallel. The method is based on formation of a training data set from an experimental signal and construction of a classifier on the basis of the value of error of the potential, that is, the difference between the measured and model values of the potential. The efficiency of parallelization of the localization problem, namely, the data distribution between processors, and the distributed training of the ensembles of decision trees are considered. Analysis of the scalability of the problem of construction of a classifier ensemble with a increase in the number of processors in the course of solution of the problem of localization of a neuron source on multiprocessor computational complexes is presented. The parallel source localization algorithm is developed for architectures with either common or distributed memory. The algorithm is realized using the MPI technology; a hybrid model of parallel calculations using MPI and OpenMPI is also discussed.     

Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method

For most parallel manipulators, the inverse kinematics is straightforward, while the direct kinematics is challenging. The latter requires the solution of a system of nonlinear equations. In this paper we use the homotopy continuation method to solve the forward and inverse kinematic problems of an offset 3-UPU translational parallel manipulator. The homotopy continuation method is a novel method which alleviates drawbacks of the traditional numerical techniques, namely; the acquirement of good initial guess values, the problem of convergence and computing time. The direct kinematics problem of the manipulator leads to 16 real solutions.     

Parallel Algorithms for Solving the Convex Minimum Cost Flow Problem

In this paper we deal with the solution of the separable convex cost network flow problem. In particular, we propose a parallel asynchronous version of the -relaxation method and we prove theoretically its correctness.We present two implementations of the parallel method for a shared memory multiprocessor system, and we empirically analyze their numerical performance on different test problems. The preliminary numerical results show a good reduction of the execution time of the parallel algorithm with the respect to the sequential counterpart.