有限元分析快速直接求解技术进展  

ADVANCES IN DIRECT SOLUTION TECHEIQUE OF FINETE ELEMENT ANALYSIS

作　　者：周洪伟[1] 吴舒[1] 陈璞[1] 

机构地区：[1]北京大学工学院,湍流与复杂系统国家重点实验室,力学与空天技术系,北京100871

出　　处：《力学进展》2007年第2期175-188,共14页Advances in Mechanics

基　　金：国家自然科学基金(10572003)~~

摘　　要：现代的有限元分析往往产生大规模的线性方程组,它的求解效率是有限元分析中最关键的一环．自20世纪90年代中期,有限元的求解技术发生了巨大的变化,传统的变带宽解法与波前法被稀疏解法所替代．这一替代为有限元分析带来了求解速度的突破,它使得1万到10万个节点的实用三维有限元分析在微机上即时求解成为现实．本文回顾非并行有限元快速直接求解技术在过去20年的发展,着重讨论了填充元优化与浮点加速运算方法,期望能引起同行的注意．Modern finite element analysis （FEA） involves usually large systems of linear equations. The efficiency in solving linear systems is the key in achieving overall efficiency of FEA. Since the 1990s, great progresses have been made in the solution of linear systems. Conventional variable bandwidth or wave frontal schemes have been replaced by various sparse schemes. That has resulted in a break through in the solution speed. With the achievements in hardware the analysis of 10 000 to 100 000 nodes finite element calculations on microcomputers becomes possible. This paper reviews developments of the direct solution in the last 20 years, emphasizing on the fill-in＇s minimization and speeding of floating point operations.

关 键 词：有限元分析 直接求解器 稀疏矩阵 高效能计算 

分 类 号：O241.6[理学—计算数学]