各向异性线弹性问题的鲁棒V-循环多重网格法

Robust V-cycle multigrid method for anisotropic linear elasticity problems

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正方形网格的区域上. 数值实验验证了理论结果.

Abstract:

A Robust V-cycle multigrid method is constructed for the linear system 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 parameterε and dependent on h in a very weakly way. 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.