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无穷扇形区域调和边值问题的重叠型区域分解法 总被引:2,自引:0,他引:2
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… 相似文献
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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. 相似文献
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平面弹性方程外问题的非重叠型区域分解算法 总被引:4,自引:0,他引:4
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… 相似文献
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Xuqiong Luo Qikui Du Hongying Huang Tianshu He 《Computers & Mathematics with Applications》2013,65(8):1129-1139
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. 相似文献
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(?)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. 相似文献
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弹性动力学问题的边界元区域分解算法 总被引:3,自引:0,他引:3
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 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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《Computer Methods in Applied Mechanics and Engineering》2005,194(45-47):4668-4684
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. 相似文献