无穷扇形区域调和边值问题的重叠型区域分解法

51．引言边界元方法在力学和科学工程计算中有着广泛的应用问．它特别适合求解无界区域上的问题［‘’，‘’1．边界元和有限元耦合［‘，＼以及作适当的人工边界处理后再在有界区域上应用有限元技术＊＼都是处理无界区域问题时常用的方法．另一方面，近年发展起来的区域分解法不仅为并行计算提供了有效手段＊’］，也为边界元方法在无界区域问题上的应用提供了新的途径．其中，无界区域上基于自然边界归化的重叠型和不重叠型区域分解算法＊’，“－‘’］，同时具备了边界元法和区域分解法的优点．它将无界区域n分解为一个很小的有界区域01…     

Stokes外问题的一种重叠型区域分解法

本文讨论了平面无界区域上Stokes问题的重叠型区域分解法.利用混合元方法求解内子区域问题得到速度和压力,再用Poisson积分公式解出外子区域的速度和压力,如此交替迭代克服区域无界性并按原始变量求出原问题的数值解.根据投影理论证明重叠型区域分解法的几何收敛性.最后给出数值例子.     

平面弹性方程外问题的非重叠型区域分解算法

１．引言 区域分解算法是八十年代兴起的偏微分方程求解新技术．基于有限元法的区域分解算法对求解有界区域问题行之有效［２,４,９］．边界元方法则是处理无界区域问题的强有力的工具［１,１０,１７］,有限元与边界元耦合法得到广泛应用 ［３,５,７］．近年又发展了基于自然边界归化的区域分解算法,特别适用于无界区域问题［８,１１,１２］．迄今这方面的文章主要是针对二维Ｐｏｉｓｓｏｎ方程及双调和方程的［１３－１６］． 本文讨论平面弹性方程的Ｄｉｒｉｃｈｌｅｔ外边值问题其中Ω是充分光滑闭曲线Г０之外的无界区域,ｕ…     

线性控制系统的无界多面体不变集

本文利用非光滑分析方法,讨论了线性控制系统的无界多面体不变集问题.当无界多面体的极方向满足一定条件时,得到了该无界多面体为一类线性控制系统弱不变集的判别方法.然后在更一般的线性控制系统下给出了无界多面体为强不变集的充分条件.最后给出两个应用实例.     

无界公平Petri网的进程表达式

Ｐｅｔｒｉ网的进程表达式是以该网系统的基本子进程集为字母的一个正规表达式．它用有限形式给出了网系统的所有（无限多个）进程的集合．作者于１９９５年给出了对任意给定的有界Ｐｅｔｒｉ网求其进程表达式的一个算法．这个算法对无界Ｐｅｔｒｉ网是不适用的,其原因在于子进程同构的概念在无界网系统中没有意义．对此,作者通过定义进程段行为等价的概念,导出了无界Ｐｅｔｒｉ网的进程表达式的一般形式,并借助无界公平网的特征     

无界：企业如何在全球互联时代生存

未来的世界和企业，将走向无界的状态．也就是人、构想和产品经由一张全球性的数字网络链接在一起。随着无界网络不断成长．以及数据量持续扩增，每一个人都会立即得到想要的几乎每一样东西。     

云计算

"智揽云端应用无界"2011年惠普云世界大会 6月10日,"智揽云端应用无界"2011年惠普云世界大会在京举行.惠普发布了,模块化数据中心,其部署速度比竞品更快,仅需12周时间,成本只有传统数据中心的四分之一.     

分式线性神经网络及其非线性逼近能力研究

提出了结构简单的分式线性神经网络,证明该种神经网络可无限逼近Rm上有界闭子集到Rn上的任意连续映射,同时,证实该种神经网络可无限逼近Rm上无界闭子集到Rn上的在无穷远有极限的任意连续映射,扩充了BP神经网络的非线性逼近能力;给出了实现分式线性神经网络逼近有界或无界区域上连续映射的反向传播算法.仿真实验表明所给出的反向传播算法可行有效.该结果为无界区域上的分类问题和决策问题的解决提供了理论基础.     

业界资讯

2012三星论坛:智无界行无疆2012年3月21日,三星电子在2012中国三星论坛上发布了以"智无界、行无疆(PushingBoundaries)"为主题的年度战略理念,突出强调了三星电子在全球范围内提出的融合互通愿景,并向中国市场发布了三星电子2012年的最新产     

单触发Petri网的一个可达性判定方法

可达性判定问题是Petri网理论研究的一个重要课题.已有文献提出通过构造Petri网的可达树或可覆盖树来分析其可达性,但其中无界量ω的引入导致了无界Petri网运行过程中的信息丢失,使其可达性无法得到判定.众所周知,对于有界Petri网,通过构造其可迭性树或可达标识图来判定其可达性是容易的,但对于大量存在的无界Petri网,找到一个能判定其可达性的一般性算法却不太容易.本文给出一个Petri网子类--单触发Petri网,并给出它的一个可达性判定方法.     

A Schwarz alternating algorithm for a three-dimensional exterior harmonic problem with prolate spheroid boundary

In this paper, we investigate a Schwarz alternating algorithm for a three-dimensional exterior harmonic problem with prolate spheroid boundary. Based on natural boundary reduction, the algorithm is constructed and its convergence is discussed. The finite element method and the natural boundary element method are alternatively applied to solve the problem in a bounded subdomain and a typical unbounded subdomain. The convergence rate is analyzed in detail for a typical domain. Two numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.     

用区域分解法计算最小曲面问题

（?）1.引 言 最小曲面问题即下列变分问题:其中（?）为Rd中有界域,Vg={u∈V:v=g于（?）（?）,V为某个函数空间.此问题及有关问题有重要应用背景,至今仍是一个研究热点,见[1]及其文献.问题（1）的 Euler方程为下述非一致非线性椭圆方程边值问题问:[3]中证明了当 时,（1）有解u∈Bv（（?））,其中BV（（??））为（?）上的有界变差函数类,其定义见下节.     

弹性动力学问题的边界元区域分解算法

In this paper, the numerical implementation of boundary element methodswith overlapping domain decomposition method for solving the Navierequations of linear elastodynamics problems in Fourier transformed domain.The computer program is compiled with Fortran 77 and several numericalexamples are presented with the test on the relation of convergence ratewith the overlapping size     

微分求积区域分裂法求解二维奇异摄动问题

本文应用微分求积法结合区域分裂法求解二维奇异摄动问题,数值实验表明,该方法简单易行,计算量少,精确度高.并且微分求积法结合区域分裂法把大型计算化成若干小型计算,避免了微分求积法导出的矩阵不是稀疏矩阵对大型计算不利的缺点.     

基于FEM／SBFEM的无穷域势流问题重叠型区域分解计算

提出了一种将有限元和比例边界有限元相结合求解无穷域势流问题的算法．用两条封闭曲线将求解域划分为存在重叠的有限和无限两个区域,在有限域和无限域上分别用有限元和比例边界有限元方法求解原问题,通过重叠区域交换数据迭代计算,直至收敛．分析了重叠区域面积的大小对计算收敛速度的影响,发现随着重叠区域面积的增大迭代次数减少,收敛速度加快．数值算例显示了算法的正确性和收敛性．本算法为求解无穷域势流问题提供了一个方法．     

A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations

We present a new domain decomposition algorithm for the parallel finite element solution of elliptic partial differential equations. As with most parallel domain decomposition methods each processor is assigned one or more subdomains and an iteration is devised which allows the processors to solve their own subproblem(s) concurrently. The novel feature of this algorithm however is that each of these subproblems is defined over the entire domain—although the vast majority of the degrees of freedom for each subproblem are associated with a single subdomain (owned by the corresponding processor). This ensures that a global mechanism is contained within each of the subproblems tackled and so no separate coarse grid solve is required in order to achieve rapid convergence of the overall iteration. Furthermore, by following the paradigm introduced in 15 , it is demonstrated that this domain decomposition solver may be coupled easily with a conventional mesh refinement code, thus allowing the accuracy, reliability and efficiency of mesh adaptivity to be utilized in a well load-balanced manner. Finally, numerical evidence is presented which suggests that this technique has significant potential, both in terms of the rapid convergence properties and the efficiency of the parallel implementation. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimized Schwarz method without overlap for the gravitational potential equation on cluster of graphics processing unit

Many engineering and scientific problems need to solve boundary value problems for partial differential equations or systems of them. For most cases, to obtain the solution with desired precision and in acceptable time, the only practical way is to harness the power of parallel processing. In this paper, we present some effective applications of parallel processing based on hybrid CPU/GPU domain decomposition method. Within the family of domain decomposition methods, the so-called optimized Schwarz methods have proven to have good convergence behaviour compared to classical Schwarz methods. The price for this feature is the need to transfer more physical information between subdomain interfaces. For solving large systems of linear algebraic equations resulting from the finite element discretization of the subproblem for each subdomain, Krylov method is often a good choice. Since the overall efficiency of such methods depends on effective calculation of sparse matrix–vector product, approaches that use graphics processing unit (GPU) instead of central processing unit (CPU) for such task look very promising. In this paper, we discuss effective implementation of algebraic operations for iterative Krylov methods on GPU. In order to ensure good performance for the non-overlapping Schwarz method, we propose to use optimized conditions obtained by a stochastic technique based on the covariance matrix adaptation evolution strategy. The performance, robustness, and accuracy of the proposed approach are demonstrated for the solution of the gravitational potential equation for the data acquired from the geological survey of Chicxulub crater.     

Generation of finite element mesh with variable size over an unbounded 2D domain

With the advance of the finite element, general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled. This paper describes an algorithm for the generation of finite element mesh of variable element size over an unbounded 2D domain by using the advancing front circle packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within an open domain. The sequence of construction of the packing circles is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation. As soon as a circle is added to the generation front, finite elements are directly generated by properly connecting frontal segments with the centre of the new circle. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of circle packing, this reduces a lot of geometrical checks for intersection with frontal segments, and a linear time complexity for mesh generation can be achieved. In case the boundary of the domain is needed, simply generate an unbounded mesh to cover the entire object. As the element adjacency relationship of the mesh has already been established in the circle packing process, insertion of boundary segments by neighbour tracing is fast and robust. Details of such a boundary recovery procedure are described, and practical meshing problems are given to demonstrate how physical objects are meshed by the unbounded meshing scheme followed by the insertion of domain boundaries.