@Article{AAMM-1-69, author = {Xiao , YingxiongShu , ShiZhang , Hongmei and Ouyang , Yuan}, title = {An Algebraic Multigrid Method for Nearly Incompressible Elasticity Problems in Two-Dimensions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {1}, pages = {69--88}, abstract = {

In this paper, we discuss an algebraic multigrid (AMG) method for nearly incompressible elasticity problems in two-dimensions. First, a two-level method is proposed by analyzing the relationship between the linear finite element space and the quartic finite element space. By choosing different smoothers, we obtain two types of two-level methods, namely TL-GS and TL-BGS. The theoretical analysis and numerical results show that the convergence rates of TL-GS and TL-BGS are independent of the mesh size and the Young's modulus, and the convergence of the latter is greatly improved on the order $p$. However, the convergence of both methods still depends on the Poisson's ratio. To fix this, we obtain a coarse level matrix with less rigidity based on selective reduced integration (SRI) method and get some types of two-level methods by combining different smoothers. With the existing AMG method used as a solver on the first coarse level, an AMG method can be finally obtained. Numerical results show that the resulting AMG method has better efficiency for nearly incompressible elasticity problems.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/209.html} }