KMS Of Academy of mathematics and systems sciences, CAS
| A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS | |
Rong, Zhijian1,2; Shen, Jie3; Yu, Haijun4,5
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| 2017 | |
| Source Publication | INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
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| ISSN | 1705-5105 |
| Volume | 14Issue:4-5Pages:762-783 |
| Abstract | 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. |
| Keyword | Sparse grid spectral element method high-dimensional problem adaptive method |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000408158100016 |
| Publisher | ISCI-INST SCIENTIFIC COMPUTING & INFORMATION |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26389 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Yu, Haijun |
| Affiliation | 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 |
| Recommended Citation 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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