有限元结构分析并行计算的若干研究进展

Some Recent Advances in the Parallel Computation of Finite Element Structural Analysis

有限元结构分析并行处理在大规模科学与工程计算中占有重要地位，本文简要介绍作者在这一领域内的研究工作及其成果。涉及单元刚度矩阵的并行计算、有限元方程组的并行直接解法、有限元方程组的并行迭代解法、结构动力分析并行直接积分法、广义特征值问题的并行算法以及ＥＢＥ（Ｅｌｅｍｅｎｔ－Ｂｙ－Ｅｌｅｍｅｎｔ）技术在有限元结构分析并行处理中的应用等研究领域。特别提出了“伪单元向量”与“单元分组技术”等新概念与新方法；首先考虑了矩阵向量积的多自由度问题；系统、深入而又全面地研究了ＥＢＥ策略在结构分析并行处理中的应用；填补了国内空白并突破了国际现有成果。

The parallel processing of finite element structural analysis plays an important role in large-scale science and engineering computations. This paper gives a brief introduction to our research work in this area,including:parallel computation for element stiffness matrices, parallel direct solutions for finite element equations, parallel iteration solutions for finite element equations, parallel direct integration algorithm in dynamic analysis of structures, parallel algorithm for generalized eigenproblems and the applications of EBE technique in finite element structural analysis. Especially,we have presented some new important concepts such as pseudo-element vector and some techniques such as element grouping;have firstly discussed the parallel computation of matrix-vector multiply in finite element structural analysis with multiple node-freedom-degrees;and have made a systematic,deep and complete study on the applications of EBE strategy in parallel processing for structural analysis. All of these have not only filled the gaps in this area in our country,but also made some breakthrough at some points in the world.