Advances in Computational Mathematics
, Volume 25, Issue 1, pp 287304
First online:
An algebraic multigrid method for finite element systems on crisscross grids
 Shi ShuAffiliated withInstitute for Computational and Applied Mathematics of Xiangtan University
 , Jinchao XuAffiliated withDepartment of Mathematics and Center for Computational Mathematics and Application of Pennsylvania State University
 , Ying YangAffiliated withInstitute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences
 , Haiyuan YuAffiliated withInstitute for Computational and Applied Mathematics of Xiangtan University
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In this paper, we design and analyze an algebraic multigrid method for a condensed finite element system on crisscross grids and then provide a convergence analysis. Crisscross grid finite element systems represent a large class of finite element systems that can be reduced to a smaller system by first eliminating certain degrees of freedoms. The algebraic multigrid method that we construct is analogous to many other algebraic multigrid methods for more complicated problems such as unstructured grids, but, because of the specialty of our problem, we are able to provide a rigorous convergence analysis to our algebraic multigrid method.
Keywords
algebraic multigrid method finite element crisscross grids convergence analysis Title
 An algebraic multigrid method for finite element systems on crisscross grids
 Journal

Advances in Computational Mathematics
Volume 25, Issue 13 , pp 287304
 Cover Date
 200607
 DOI
 10.1007/s104440047627y
 Print ISSN
 10197168
 Online ISSN
 15729044
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 algebraic multigrid method
 finite element
 crisscross grids
 convergence analysis
 Industry Sectors
 Authors

 Shi Shu ^{(001)}
 Jinchao Xu ^{(002)}
 Ying Yang ^{(003)}
 Haiyuan Yu ^{(001)}
 Author Affiliations

 001. Institute for Computational and Applied Mathematics of Xiangtan University, China
 002. Department of Mathematics and Center for Computational Mathematics and Application of Pennsylvania State University, USA
 003. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, China