基于超节点LDL分解的大规模结构计算  

Large scale structure computation based on supernode LDL factorization

作　　者：赖智超 罗晓群[1] 张其林[1] 

机构地区：[1]同济大学土木工程学院,上海200092

出　　处：《计算机辅助工程》2014年第2期46-52,共7页Computer Aided Engineering

基　　金：上海市科技人才计划(11XD1404900)

摘　　要：采用列压缩稀疏(Compressed Sparse Column,CSC)矩阵存储策略对矩阵LDL分解前进行填充元优化排序;基于消去树进行LDL符号分解,使之独立于数值分解,避免多余的内存消耗,减少不必要的数值运算.利用矩阵非零元的分布特性分析并实现超节点LDL分解算法,将稀疏矩阵的分解运算变为一系列稠密矩阵运算,并使用优化的BLAS函数库加速分解.测试表明:算法在成倍地提高计算速度的同时进一步降低内存消耗,适用于大规模的结构计算.The fill-element optimization ordering is performed on matrix before LDL factorization by Compressed Sparse Column（ CSC ） storage strategy; the LDL symbolic faetorization is performed on the basis of elimination tree to be independent of the numerical factorization, which can avoid redundant memory usage and unnecessary numerical calculation. Using distribution characteristics of matrix nonzero elements, the supernode LDL faetorization algorithm is analyzed and implemented, and the resolve operation of sparse matrix is changed to a series of dense matrix operation, which is also accelerated with the optimized BLAS function library. The test shows that the algorithm can improve the computation speed exponentially and decrease the memory consumption at the same time. So the algorithm can be applied to the practical large scale structure computation.

关 键 词：稀疏矩阵 LDL分解 消去树 符号分解 超节点 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]