大型稀疏线性方程组符号LU分解法

计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (28): 29-30.

大型稀疏线性方程组符号LU分解法

张永杰,孙秦

西北工业大学航空学院,西安 710072

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2007-10-01 发布日期:2007-10-01
通讯作者: 张永杰

Symbol LU decomposition method of large scale sparse linear equations

ZHANG Yong-jie,SUN Qin

School of Aeronautics,NPU,Xi’an 710072,China

Received:1900-01-01 Revised:1900-01-01 Online:2007-10-01 Published:2007-10-01
Contact: ZHANG Yong-jie

摘要/Abstract

摘要： 基于有限元总刚矩阵的大规模稀疏性、对称性等特性,采用全稀疏存储结构以及最小填入元算法,使得计算机的存储容量达到最少。为了节省计算机的运算时间,对总刚矩阵进行符号LU分解方法,大大减少了数值求解过程中的数据查询。这种全稀疏存储结构和符号LU分解相结合的求解方法,使大规模稀疏线性化方程组的求解效率大大提高。数值算例证明该算法在时间和存贮上都较为占优,可靠高效,能够应用于有限元线性方程组的求解。

关键词: 大型稀疏线性方程组, 全稀疏存贮策略, 符号LU分解

Abstract: Based on large scale sparse and symmetrical matrix of FEM equations,this paper takes the fully sparse strategy and minimum full-in entries algorithm such that makes lowest storing requirement to computer.For the sake of CPU operational time saving to accesses data in matrix decomposition,a symbol LU decomposing method is applied.The combination of the symbol LU decomposition and fully sparse storage structure can greatly improve the algorithmic efficiency for FEM solution of large scale sparse linear equation group.Numerical examples show that the method is available,effective and predominant for time and storage.Therefore it is applicable to solve systems of linear equations from FEM.

Key words: large scale sparse linear equations, fully sparse strategy, symbol LU decomposition

张永杰,孙秦. 大型稀疏线性方程组符号LU分解法[J]. 计算机工程与应用, 2007, 43(28): 29-30.

ZHANG Yong-jie,SUN Qin. Symbol LU decomposition method of large scale sparse linear equations[J]. Computer Engineering and Applications, 2007, 43(28): 29-30.