A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

	A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS
	Rong, Zhijian 1,2; Shen, Jie 3; Yu, Haijun4,5
	2017
发表期刊	INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
ISSN	1705-5105
卷号	14 期号:4-5 页码:762-783
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.
关键词	Sparse grid spectral element method high-dimensional problem adaptive method
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000408158100016
出版者	ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26389
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.