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An algebraic multigrid method for higher-order finite element discretizations
Shu, S; Sun, D; Xu, J
2006-06-01
发表期刊COMPUTING
ISSN0010-485X
卷号77期号:4页码:347-377
摘要In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.
关键词algebraic multigrid methods high-order finite element unstructured grids geometric-based
DOI10.1007/s00607-006-0162-6
语种英语
WOS研究方向Computer Science
WOS类目Computer Science, Theory & Methods
WOS记录号WOS:000238632500003
出版者SPRINGER WIEN
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/2573
专题中国科学院数学与系统科学研究院
通讯作者Shu, S
作者单位1.Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China
2.Acad Sinica, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
3.Xiangtan Univ, Inst Computat & Appl Math, Xiangtan 411105, Hunan, Peoples R China
4.Penn State Univ, Dept Math, Ctr Computat Math & Applicat, University Pk, PA 16802 USA
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Shu, S,Sun, D,Xu, J. An algebraic multigrid method for higher-order finite element discretizations[J]. COMPUTING,2006,77(4):347-377.
APA Shu, S,Sun, D,&Xu, J.(2006).An algebraic multigrid method for higher-order finite element discretizations.COMPUTING,77(4),347-377.
MLA Shu, S,et al."An algebraic multigrid method for higher-order finite element discretizations".COMPUTING 77.4(2006):347-377.
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