二维泊松方程边值问题有限差分方程的病态结构和最优预条件子  

Ill-condition Structure and Optimal Preconditioner of Finite Difference Equation for 2D Poisson Equation Boundary Value Problems

作　　者：张衡[1,2] 郑汉垣 ZHANG Heng;ZHENG Hanyuan(Fuqing Branch of Fujian Normal University,Fuqing,Fujian,350300,China;School of Communication and Design,Longyan University,Longyan,Fujian,364012,China)

机构地区：[1]福建师范大学福清分校无损检测技术福建省高校重点实验室,福建福清350300 [2]福建师范大学福清分校电子与信息工程学院,福建福清350300 [3]龙岩学院传播与设计学院,福建龙岩364012

出　　处：《福建师大福清分校学报》2018年第5期1-6,共6页Journal of Fuqing Branch of Fujian Normal University

基　　金：福建省自然科学基金(2014J01006;2015J01587)

摘　　要：基于结构分析的思想,讨论大规模病态稀疏线性方程的病态机理和预处理原理,定义该方程组的病态结构、病态因子、去病因子.针对病态结构,设计去病因子,以去病因子为预条件子,并对预条件子的性能进行定量分析,结果表明去病因子是最优预条件子,该预条件子的使用,几乎不增加迭代的计算量,预处理后方程组的主体保持正定对称,条件数接近常数.Ill-condition sparse linear system. Depending on the idea of structural analysis, this paper discusses the ill-condition mechanism and preconditioning principle of the equation. The definitions of ill- condition structure, ill-condition factors and the cure factor of the equations are offered. We propose a cure factor according to the ill-condition structure and treat this cure factor as the preconditioner. In addition, quantitative analysis for the proposed preconditioner is conducted. The analysis results show that the cure factor is optimal preconditioner, the positive definite symmetry of the equations is maintained and condition number is close to a constant after pretreatment without causing additional computing.

关 键 词：病态机理 病态结构 病态因子 去病因子 预处理 

分 类 号：O24[理学—计算数学]