A geometric-based algebraic multigrid method for higher-order finite element equations in two-dimensional linear elasticity

In this paper, we will discuss the geometric‐based algebraic multigrid (AMG) method for two‐dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two‐level method is proposed by analyzing the relationship between the linear finite element space and higher‐or...

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Published inNumerical linear algebra with applications Vol. 16; no. 7; pp. 535 - 559
Main Authors Xiao, Yingxiong, Shu, Shi, Zhao, Tuyan
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.07.2009
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ISSN1070-5325
1099-1506
DOI10.1002/nla.629

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Summary:In this paper, we will discuss the geometric‐based algebraic multigrid (AMG) method for two‐dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two‐level method is proposed by analyzing the relationship between the linear finite element space and higher‐order finite element space. And then a geometric‐based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high‐order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd.
Bibliography:istex:B17E18C58280AA2C4962ED7887A17988E06A024C
Provincial Natural Science Foundation of Hunan - No. 07JJ6004
Key Project of Chinese Ministry of Education and Scientific Research Fund of Hunan Provincial Education Department - No. 208093; No. 07A068
ark:/67375/WNG-P5T1PMTX-G
Basic Research Program of China - No. 2005CB321702
ArticleID:NLA629
National Natural Science Foundation of China - No. NSF-10771178; No. NSF-10672138; No. NSAF-10676031
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.629