Multi-neighboring grids schemes for solving PDE eigen-problems

ISCAS OpenIR

	Multi-neighboring grids schemes for solving PDE eigen-problems
	Sun JiaChang
	2013
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	56 期号:12 页码:2677-2700
摘要	Instead of most existing postprocessing schemes, a new preprocessing approach, called multineighboring grids (MNG), is proposed for solving PDE eigen-problems on an existing grid G(Delta). The linear or multi-linear element, based on box-splines, are taken as the first stage (K1Uh)-U-h = lambda(1M1Uh)-M-h-U-h. In this paper, the j-th stage neighboring-grid scheme is defined as (KjUh)-U-h = lambda(jMjUh)-M-h-U-h, where K-j(h) := M-j-1(h) circle times K-1(h) and (MjUh)-U-h is to be found as a better mass distribution over the j-th stage neighboring-grid G(Delta), and K-j(h) can be seen as an expansion of K-1(h) on the j-th neighboring-grid with respect to the (j - 1)-th mass distribution M-j-1(h). It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even (2j + 2)-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j <= 3.; Instead of most existing postprocessing schemes, a new preprocessing approach, called multineighboring grids (MNG), is proposed for solving PDE eigen-problems on an existing grid G(Delta). The linear or multi-linear element, based on box-splines, are taken as the first stage (K1Uh)-U-h = lambda(1M1Uh)-M-h-U-h. In this paper, the j-th stage neighboring-grid scheme is defined as (KjUh)-U-h = lambda(jMjUh)-M-h-U-h, where K-j(h) := M-j-1(h) circle times K-1(h) and (MjUh)-U-h is to be found as a better mass distribution over the j-th stage neighboring-grid G(Delta), and K-j(h) can be seen as an expansion of K-1(h) on the j-th neighboring-grid with respect to the (j - 1)-th mass distribution M-j-1(h). It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even (2j + 2)-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j <= 3.
收录类别	SCI
关键词	Pde Eigen-problem Discrete Rayleigh Quotient Multi-neighboring Grids Schemes B-splines
部门归属	Chinese Acad Sci, Inst Software, Sci Computat Lab, Beijing 100080, Peoples R China.
语种	英语
WOS记录号	WOS:000328279100015
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16897
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Sun JiaChang. Multi-neighboring grids schemes for solving PDE eigen-problems[J]. SCIENCE CHINA-MATHEMATICS,2013,56(12):2677-2700.
APA	Sun JiaChang.(2013).Multi-neighboring grids schemes for solving PDE eigen-problems.SCIENCE CHINA-MATHEMATICS,56(12),2677-2700.
MLA	Sun JiaChang."Multi-neighboring grids schemes for solving PDE eigen-problems".SCIENCE CHINA-MATHEMATICS 56.12(2013):2677-2700.