基于模型减缩的并行共轭梯度算法研究

Model Reduction-Based Parallel Conjugate Gradient Method

有限元并行计算被应用于求解大规模工程问题。为进一步提高计算效率,将模型减缩方法引入到并行计算区域划分步骤中,采用共轭梯度法,推导了适用于分布式并行环境的模型减缩并行算法。该方法在模型减缩的基础上,将边界节点进一步分为"本地节点"和"共享节点",各任务处理器仅交换"共享节点"相关数据,降低了数据交换量,同时仅保存降阶后的区域矩阵,减少了内存存储。编制了MPI并行计算程序,并通过算例对该方法和普通有限元并行方法进行了比较,验证了算法的有效性。

The finite element parallel computation is applied to analysis of largescale engineering prob lems. To make further improvement of computation efficiency, the model reduction method was employed in the procedure of parallel computation domain decomposition, then the parallel computation method with conjugate gradient arithmetic was derived for distributed parallel environment. The method divides the boundary nodes of one domain into ＂local nodes＂ and ＂common nodes＂ and only the data about ＂common nodes＂ are exchanged among the parallel processors. In this way, it reduces communication traffic. More over, it saves the reduction model＇s matrices to reduce the requirement for storage. The MPI parallel computation program was developed in the numerical example. By comparison between the method men tioned above and the general finite element parallel computation, the results testify the validity of the method.