基于Hadoop MapReduce的大规模线性有限元法并行实现

PARALLEL IMPLEMENTATION OF LARGE-SCALE LINEAR FEM BASED ON HADOOP MAPREDUCE FRAMEWORK

面对越来越复杂的工程问题,单机上的有限元计算不能达到完全解决问题的程度,可以考虑利用新兴云计算技术来解决。设计合适的杆单元数据结构,提出基于MapReduce框架的线性有限单元法并行算法,包括总体刚度阵组装和CG法求解线性方程组。在6节点Hadoop实验集群上,通过大规模空间桁架结构进行数值验证。结果表明采用该算法求解大规模空间桁架结构简洁、易用;在总刚组装阶段,网格模型越大,计算节点越多,计算性能越好;但求解方程组阶段,计算性能不理想,有待改善。

In the face of increasingly complex engineering problems, we cannot completely solve these problems through finite element method （FEM） on a single machine, but we can consider using emerging cloud computing technology. In this paper, we design an appropriate data structure of truss element and propose a parallel algorithm of linear finite element method based on MapReduce framework, including assembling global stiffness matrix and conjugate gradient （CG） method for solving linear equation groups. On the six-node Hadoop experimental cluster, numerical verification is carried out large-scale spatial through large-scale spatial truss structures. The results show that it is simple and easy to solve truss structures by using the proposed algorithm. At the stage of assembling global stiffness matrix, as the size of the mesh model and the number of cluster＇ s nodes increase, the computing performance becomes better. However, at the stage of solving equation groups, the computing performance is not ideal and should be improved in the future.