用并行CG_DY算法进行圆柱体压力场测定

Determination of stress field on the cylindrical bar by parallel CG_DY

给出了由Dai和Yuan提出的非线性共轭梯度算法(CG_DY)的并行实现,并应用并行CG_DY算法在高性能计算机上求解圆柱体压力场测定的问题,比较了曙光2000和深腾6800的性能。数值计算给出了满意的结果,发现并行CG_DY算法在最优化问题的设计中具有很好的性质,并显示其具有很好的可扩展性。

Nonlinear conjugrate gradient method proposed by Dai and Yuan, called CG_DY, is implemented in parallel in this paper. CGDY uses different method to compute the key parameter β. First, the algorithm principle and programming method are discussed. Second, parallel line search and vector inner product are intoduced into the algorithm implementation, which is applied to slove the elastic plastic torsion problem which arises from the determination of the stress field on an infinitely long cylindrical bar. A finite element approximation to the torsion problem is used and one problem with up to 1, 048, 576 variables is generated. Finally, we show the performance results on the Dawning 2000 and Deep Comp 6800 with the number of processors from 1 to 64, respectively. From the results, we can see that the method has good scalability and parallel efficiency.