各向异性线弹性问题的鲁棒V-循环多重网格法（英文）  

Robust V-cycle multigrid method for anisotropic linear elasticity problems

作　　者：白艳红 吴永科 覃艳梅 BAI Yan-Hong;WU Yong-Ke;QIN Yan-Mei(School of Sciences,Xihua University,Chengdu 610039,China;School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China;Key Laboratory of Numerical Simulation in the Sichuan Provincial College&School of Maths and Informations Science,Neijiang Normal University,Neijiang 641112,China)

机构地区：[1]西华大学理学院,成都610039 [2]电子科技大学数学科学学院,成都611731 [3]内江师范学院四川省高等学校数值仿真重点实验室/数学与信息科学学院,内江641112

出　　处：《四川大学学报（自然科学版）》2019年第5期819-826,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11701481)

摘　　要：本文对各向异性线弹性方程的双线性有限元法离散系统构造一种“鲁棒”的V-循环多重网格法.通过Xu-Zikatanov(XZ)等式,本文得到了所构造多重网格算法的不依赖于各向异性参数ε,而弱依赖于h的拟最优收敛性.由于分析中未用到线弹性方程的“正则性”假设,该收敛性结果可以推广到一般的可剖分成矩形网格的区域上.数值实验验证了理论结果.A robust V-cycle multigrid method is constructed for the linear systems arising from the bilinear finite element discretization of anisotropic linear elasticity equations.By using the Xu-Zikatanov(XZ)identity,quasi-optimal convergence of the method is established in the sense that the multigrid method is independent of the parameterεand weakly dependent on h.Since the“regularity assumption”is not used in the analysis,the results can be extended to domains consisting of rectangles.Numerical experiments confirm the theoretical results.

关 键 词：线弹性 各向异性 双线性元 多重网格法 

分 类 号：O241.82[理学—计算数学]