An algebraic multigrid method for higher-order finite element discretizations
文献类型：期刊论文
| 作者 | Shu, S; Sun, D; Xu, J |
| 刊名 | COMPUTING
 |
| 出版日期 | 2006-06-01 |
| 卷号 | 77期号:4页码:347-377 |
| 关键词 | algebraic multigrid methods high-order finite element unstructured grids geometric-based |
| ISSN号 | 0010-485X |
| DOI | 10.1007/s00607-006-0162-6 |
| 英文摘要 | 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. |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000238632500003 |
| 出版者 | SPRINGER WIEN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2572]  |
| 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 |
| 推荐引用方式 GB/T 7714 | 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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