一维问题一次形函数有限元方程的条件数与预处理  

Condition Number and Preprocess of the Finite Element Equation of One Dimensional Problem with Linear Shape Function

作　　者：张衡[1] 

机构地区：[1]福建师范大学福清分校电子与信息工程学院,福建福清350300

出　　处：《福建师大福清分校学报》2016年第2期1-3,共3页Journal of Fuqing Branch of Fujian Normal University

基　　金：福建省自然科学基金(2014J01006)

摘　　要：科学计算和工程应用中经常遇到大型稀疏病态线性方程组的求解问题,解决该问题的关键是通过预处理来降低条件数。讨论了求解积分形式的两点边值问题时,利用一次形函数形成的有限元方程组。通过研究该方程组的特别结构,分析了该方程的条件数。将系数矩阵的大范数部分分解成四个结构简单的矩阵乘积,利用这个分解,提出预处理方法,大大降低了条件数。Solving the large sparse ill-conditioned linear equations are often the problem in scientific computing and engineering applications. The key to solve the problem is reducing the condition number by preprocessing. The finite element equations formed in solving two-point boundary value problems of integral form using finite element method based on linear shape function are discussed. The condition number of the finite element equations is analyzed by studying the special structure of the equation. The big norm part of the coefficient matrix is decomposed into product of four simple structure matrices. The preprocess method are obtainedby using the decomposition, and the condition number is reduced greatly.

关 键 词：稀疏线性方程组 特别结构 条件数 预处理 

分 类 号：O24[理学—计算数学]