Domain decomposition methods for large linearly elliptic three-dimensional problems
Domain decomposition methods for large linearly elliptic three-dimensional problems
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DOI：
10.1016/0377-0427(91)90150-i
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发表时间：
1991-02
影响因子：
2.4
通讯作者：
P. Tallec;Y.H.De Roeck;M. Vidrascu
中科院分区：
文献类型：
--
作者：
P. Tallec;Y.H.De Roeck;M. Vidrascu
在当今的大规模并行计算机中，用区域分解技术求解大型问题的思想显得特别有吸引力。但是这种技术在并行计算机上的性能取决于所提出算法的数值效率和其并行实现的效率。本文提出的方法将计算域分成任意形状的非结构化子域，并使用关联的跟踪运算符求解接口上的未知数（Steklov-Poincaré算子或有限元离散后的Schur补矩阵）和预条件共轭梯度法。该算法涉及Dirichlet问题和Neumann问题的求解，定义在每个子域上，可以并行求解.该方法已在CRAY 2多任务计算机和INTEL超立方体计算机上实现.它是在一个大规模的，工业的，病态的，三维线性弹性问题，这给出了一个公平的指示，其性能在真实的生活环境中进行了测试。在这种情况下，所提出的方法在两台机器上都具有可操作性和竞争力：与标准技术相比，它产生更快的结果，而内存需求要少得多。
The idea of solving large problems using domain decomposition technique appears particularly attractive on present day large-scale parallel computers. But the performance of such techniques used on a parallel computer depends on both the numerical efficiency of the proposed algorithm and the efficiency of its parallel implementation.The approach proposed herein splits the computational domain in unstructured subdomains of arbitrary shape, and solves for unknown on the interface using the associated trace operator (the Steklov-Poincaré operator on the continuous level or the Schur complement matrix after a finite element discretization) and a preconditioned conjugate gradient method. This algorithm involves the solution of Dirichlet and of Neumann problems, defined on each subdomain and which can be solved in parallel.This method has been implemented on a CRAY 2 computer using multitasking and on an INTEL hypercube. It was tested on a large scale, industrial, ill-conditioned, three-dimensional linear elasticity problem, which gives a fair indication of its performance in a real life environment. In such situations, the proposed method appears operational and competitive on both machines: compared to standard techniques, it yields faster results with far less memory requirements.