三维弹性力学问题中有限元方程的预处理方法  

A Preconditioned Method for the Finite Element Equations of Three Dimensional Elasticity Problems

作　　者：肖映雄[1] 张平[1] 谢学斌[2] 

机构地区：[1]湘潭大学基础力学与材料工程研究所,湖南湘潭411105 [2]中南大学资源与安全工程学院,湖南长沙410083

出　　处：《湖南大学学报（自然科学版）》2004年第6期95-99,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(10372087);湖南省教育厅资助项目(03C451)

摘　　要：针对三维弹性问题中有限元方程的数值求解,建立了一类简单且实用的代数多重网格预处理共轭梯度法(AMG＿CG法),详细描述了相应代数多重网格方法的粗化技术及网格转移算子的构造.由于该预处理方法能有效地降低刚度矩阵的条件数,使刚度矩阵的谱分布更集中,从而大大提高了计算效率.数值结果表明,AMG＿CG法对求解三维弹性问题有限元方程是十分有效和健壮的.We constructed a simple but applicable algebraic multigrid-preconditioned CG algorithm(AMG_CG)for the solution of the finite element equations of three dimensional elasticity problems. The related coarsing technique and the design of interpolation operator were described in detail. Since this method can reduce the condition numbers of the stiffness matrix, it is effective for the solution of three dimensional elastic problems. Numerical results have shown that this AMG_CG method is very efficient and robust.

关 键 词：三维弹性 代数多重网格 转移算子 预处理 

分 类 号：TB115[理学—数学] O343.3[理学—应用数学]