福州大学学报（自然科学版）2017，Vol.45Issue(5)：617-622,6.DOI:10.7631/issn.1000-2243.2017.05.0617
两点边值问题2次Lagrange形函数有限元方程的条件数和预处理
Condition number and preprocess of the finite element equation of two point boundary value problems with 2-degree Lagrange shape function
摘要
Abstract
For the ill conditioned problem of the positive definite symmetric five diagonal finite element systems formed solving two-point boundary value problems of integral form using finite element method based on 2-degree Lagrange shape function.The method for looking up the reason producing ill called pathogenic factor and designing preconditioner called eliminate ill factor to eliminating the ill-condition was obtained based on the special structure of the systems.The results of the analysis shows that pretreatment using the eliminate ill factor,can guarantee positive definite symmetry of the coefficient matrix,and the condition number is close to 1 after pretreatment without causing more computing.关键词
病态五对角方程组/特别结构/条件数/预条件子/边值问题Key words
ill conditioned five diagonal equations/special structure/condition number/preconditioner/boundary value problems分类
数理科学引用本文复制引用
张衡..两点边值问题2次Lagrange形函数有限元方程的条件数和预处理[J].福州大学学报（自然科学版）,2017,45(5):617-622,6.基金项目
福建省自然科学基金资助项目(2014J01006) （2014J01006）
