岩土工程百万以上自由度有限元并行计算Parallelcomputationoffinite.PDF

岩土工程百万以上自由度有限元并行计算 张友良 冯夏庭 中国科学院武汉岩土力学研究所 摘 要 讨论了大规模有限元并行计算需要解决的并行策略、大量数据的分布存储、方程组 迭代求解和程序实现等问题。采用区域分解的“分而治之”的并行策略实现有限元并行。结 合区域分解并行策略，将每个子区域的数据信息存储在相应的各个计算机上，实现存储局部 化，大大减少并行计算中的通讯量，同时可以实现大规模计算。采用 Schur 补和共轭梯度法 来实现方程组的并行求解，解决岩土有限元病态方程组的求解。采用面向对象的编程技术开 发了并行有限元程序。应用对两个大规模算例进行了并行计算，得到了较好的计算结果。 关键词 并行有限元 区域分解 岩土工程 Parallel computation of finite element model with millions of DOF in geotechnical engineering Zhang Youliang Feng Xiating Institute of Rock and Soil Mechanics, Chinese Academy of Sciences Abstract: The parallel strategies of finite element method, the distributed storage of abundant data, the convergence speed of iterative solution of large scale linear equations and the implementation of parallel finite element method are discussed. We use domain decomposition method (“divide and conquer” strategy) to achieve the parallization of FEM. In combination of domain decomposition strategy, we store the data linking with each subdomain in each processor. So the data locality not only can reduce the communication, but also increase the scale of the computation. We adopt Schur complement and preconditioning conjugated gradient (PCG) method to fulfill parallel solution of linear equations with bad condition number. We utilize object-oriented programming method to develop our parallel FEM software. Two examples are used to discuss the efficiency of the parallel software. The results show that the software has high performance. Key words: parallel finite element method, domain decomposition, geotechnical engineering 1 引言 以上结点），系统方程组十分巨大，方程组 有限元数值计算是研究岩土工程问题 的条件数随其阶数增加而急剧增加。同时， 的一种