一种充分局部化的子结构并行分析方法

机群系统是一种低成本的松散耦合型分布式并行平台,它要求并行算法设计时遵循"分而治之"的原则,尽量降低节点任务之间的相关性。本文在FETI方法和A-FETI方法的基础上,直接从力学概念出发,提出了一种充分局部化的FETI方法。该方法在进行子域界面处理时引入三重变量:界面节点位移、界面节点力、分区框架上耦合节点位移,由此得到一组近似解耦的界面方程,使得各个子域的计算相对于经典的FETI算法更加独立。对得到的界面方程采用预处理共轭投影梯度法(PCPG)并行求解,所采用的预处理算子为局部化的集中型Dirichlet算子。分别在自建的两套4节点PC机群上进行了两组算例的验算,结果表明,本文方法具有很好的计算精度和收敛速度。并行加速比达到3.76。

A localized FETI method for structural parallel analysis

PC Cluster system is a low cost parallel computing platform that requires parallel algorithm should obey the rule of "divide and conquer" to improve parallel efficiency.In this paper,based on the FETI(Finite element tearing and interconnecting) method and A-FETI method,a localized FETI(L-FETI) method derived directly from mechanical concept.In this method,three field variables are introduced to describe the interface of the subdomains: interface node displacements,interface node forces,coupled node displacements of partitioned frame.The interface equation obtained from this method has a nearly decoupled form,so that the correlations of subdomain computing are weak.The obtained interface equation can be parallel solved by PCPG method in which a lumped Dirichlet preconditioner is applied.Two numerical examples are performed on two handmade 4-node PC Clusters respectively to verify the parallel efficiency of this method.The results show that good accuracy and parallel speedup ratio can be obtained by the proposed method with a maximum parallel speedup ratio of 3.76.