@Article{AAMM-1-1,
author = {Yingxiong, Xiao and Shu, Shi and Zhang, Hongmei and Yuan, Ouyang},
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 = {<p style="text-align: justify;">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&#39;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&#39;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/2009-AAMM-209},
url = {https://global-sci.com/article/73674/an-algebraic-multigrid-method-for-nearly-incompressible-elasticity-problems-in-two-dimensions}
}