带间断系数椭圆问题的P_1非协调四边形元的加性Schwarz方法  

AN ADDITIVE SCHWARZ PRECONDITIONER FOR P_1 NONCONFORMING QUADRILATERAL FINITE ELEMENT METHODSFOR ELLIPTIC EQUATIONS WITH JUMP COEFFICIENTS

作　　者：王锋[1] 陈金如[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,南京210097

出　　处：《计算数学》2009年第2期209-224,共16页Mathematica Numerica Sinica

基　　金：国家重点基础研究专项经费(项目号2005CB321704);国家自然科学基金(项目号10871100);江苏省自然科学基金重点项目(项目号BK2006725);江苏省自然科学基金(项目号BK2008426)资助项目.

摘　　要：本文讨论了带间断系数的二阶椭圆问题的P_1非协调四边形元的加性Schwarz方法.通过分析加性Schwarz预处理后系统的特征值分布,我们证明了除少数小特征值外,其余所有特征值都有正的关于间断系数和网格尺寸拟一致的上下界.数值试验验证了我们的结论.In this paper, we propose a two level additive Schwarz preconditioner for P1 nonconforming quadrilateral finite element approximations of elliptic equations with jump coefficients. By analyzing the eigenvalue distribution of the additive Schwarz preconditioned systems, we prove that except a small number of eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump coefficients and meshsize. Therefore, we can get that the convergence rate of the preconditioned conjugate gradient methods is quasi uniform with respect to the large jump and meshsize. Finally, some numerical experiments are presented to confirm our theoretical results.

关 键 词：非协调元 间断系数 区域分解 加性Schwarz方法 

分 类 号：O241.82[理学—计算数学]