一种改进的基于线性有限元并行计算的追赶算法

摘要

With the expansion of the scale of the finite element analysis, the finite element parallel computation is playing an increasingly prominent role.At present, the researches on finite element parallel computation are mainly concentrated on the pre-processing phase. Those researches aim to reduce the communication overhead and improve the homogeneous degree. However, the researches on calculation phase is rare. Problem is that most of calculation cost is in this phase. In this paper, stiffness matrix decomposition is studied. After comparing the different matrix decomposition algorithms, a new method based on Thomas algorithm is proposed. The numerical experiments indicate that, this method highly improves the performance of finite element analysis with low computational complexity and memory overhead.%　　随着有限元计算规模的扩大，有限元并行计算的作用日益凸显。目前，对于有限元计算的并行处理的研究，主要集中在有限元计算的前置处理阶段，即有限元模型建立和网格划分阶段；研究以提高每个处理器所负责的子结构中的单元节点数的均匀程度及减少通信开销为目标。然而，鲜有对有限元分析的计算求解阶段的并行处理进行深入研究，而有限元并行计算绝大部分都在此阶段完成。本文就是针对该问题，对线性有限元并行计算求解阶段需要处理的刚度矩阵进行分析，依据刚度矩阵的特点和比较各种矩阵分解算法的优劣之后，提出一种优化的并行计算策略。经过验证，在对刚度矩阵的计算进行分布式并行处理后，有限元分析的计算速度有明显提高。