A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS | |
Rong, Zhijian1,2; Shen, Jie3; Yu, Haijun4,5 | |
刊名 | INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING |
2017 | |
卷号 | 14期号:4-5页码:762-783 |
关键词 | Sparse grid spectral element method high-dimensional problem adaptive method |
ISSN号 | 1705-5105 |
英文摘要 | We develop a sparse grid spectral element method using nodal bases on Chebyshev-Gauss-Lobatto points for multi-dimensional elliptic equations. Since the quadratures based on sparse grid points do not have the accuracy of a usual Gauss quadrature, we construct the mass and stiffness matrices using a pseudo-spectral approach, which is exact for problems with constant coefficients and uniformly structured grids. Compared with the regular spectral element method, the proposed method has the flexibility of using a much less degree of freedom. In particular, we can use less points on edges to form a much smaller Schur-complement system with better conditioning. Preliminary error estimates and some numerical results are also presented. |
资助项目 | NSFC[11201393] ; Fujian Provincial Natural Science[2013J05019] ; AFOSR[FA9550-16-1-0102] ; NSF[DMS-1620262] ; China National Program on Key Basic Research Project[2015CB856003] ; NNSFC[91530322] ; NNSFC[11371358] ; NNSFC[11101413] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | ISCI-INST SCIENTIFIC COMPUTING & INFORMATION |
WOS记录号 | WOS:000408158100016 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26388] |
专题 | 计算数学与科学工程计算研究所 |
通讯作者 | Yu, Haijun |
作者单位 | 1.Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China 2.Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China 3.Purdue Univ, Dept Math, W Lafayette, IN 47906 USA 4.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Rong, Zhijian,Shen, Jie,Yu, Haijun. A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2017,14(4-5):762-783. |
APA | Rong, Zhijian,Shen, Jie,&Yu, Haijun.(2017).A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,14(4-5),762-783. |
MLA | Rong, Zhijian,et al."A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 14.4-5(2017):762-783. |
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