三维椭圆问题三次有限元方程的代数多层网格法  

AMG METHOD FOR CUBIC FINITE-ELEMENT DISCRETIZATIONS OF ELLIPTIC PROBLEMS IN THREE DIMENSIONS

作　　者：张红梅[1] 肖映雄[2] 舒适[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《数值计算与计算机应用》2008年第4期277-290,共14页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金资助项目(10771178;10676031);教育部重点项目和湖南省教育厅重点项目(208093;07A068);高性能科学计算研究资助项目(2005CB321702);湖南省自然科学基金联合基金资助项目(07JJ6004).

摘　　要：通过分析三次有限元空间与线性有限元空间之间的关系,提出了一种求解三维椭圆问题三次有限元方程的两水平方法.然后,通过调用现有的代数多层网格(AMG)法求解粗水平方程,建立了求解三次有限元方程的AMG法,并对其收敛性进行了严格的理论分析.数值实验结果表明,本文设计的AMG方法对求解三维椭圆问题三次有限元方程具有很好的计算效率和鲁棒性.A two-level method is first proposed in this paper for cubic finite-element discretizations of elliptic problems with jump coefficients in three dimensions by analyzing the relationship between the linear finite-element space and cubic finite-element space. And then, an alge- braic multigrid （AMG） method is obtained with the existing solver used as a solver on the first coarse level. Furthermore, the corresponding theoretical analysis is presented for the convergence of the constructed AMG algorithm. The results of various numerical experiments are shown that the resulting AMG method is robust and efficient for solving finite element equations discretized by cubic elements in three dimensions.

关 键 词：代数多层网格 三次元 两水平方法 四面体剖分 

分 类 号：O241.82[理学—计算数学] O175.26[理学—数学]