中国科学院软件研究所机构知识库
Advanced  
ISCAS OpenIR  > 软件所图书馆  > 期刊论文
Title:
Multi-neighboring grids schemes for solving PDE eigen-problems
Author: Sun JiaChang
Keyword: PDE eigen-problem ; discrete Rayleigh quotient ; multi-neighboring grids schemes ; B-splines
Source: SCIENCE CHINA-MATHEMATICS
Issued Date: 2013
Volume: 56, Issue:12, Pages:2677-2700
Indexed Type: SCI
Department: Chinese Acad Sci, Inst Software, Sci Computat Lab, Beijing 100080, Peoples R China.
Abstract: 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.
English Abstract: 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.
Language: 英语
WOS ID: WOS:000328279100015
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16897
Appears in Collections:软件所图书馆_期刊论文

Files in This Item:

There are no files associated with this item.


Recommended Citation:
Sun JiaChang. Multi-neighboring grids schemes for solving PDE eigen-problems[J]. SCIENCE CHINA-MATHEMATICS,2013-01-01,56(12):2677-2700.
Service
Recommend this item
Sava as my favorate item
Show this item's statistics
Export Endnote File
Google Scholar
Similar articles in Google Scholar
[Sun JiaChang]'s Articles
CSDL cross search
Similar articles in CSDL Cross Search
[Sun JiaChang]‘s Articles
Related Copyright Policies
Null
Social Bookmarking
Add to CiteULike Add to Connotea Add to Del.icio.us Add to Digg Add to Reddit
所有评论 (0)
暂无评论
 
评注功能仅针对注册用户开放,请您登录
您对该条目有什么异议,请填写以下表单,管理员会尽快联系您。
内 容:
Email:  *
单位:
验证码:   刷新
您在IR的使用过程中有什么好的想法或者建议可以反馈给我们。
标 题:
 *
内 容:
Email:  *
验证码:   刷新

Items in IR are protected by copyright, with all rights reserved, unless otherwise indicated.

 

 

Valid XHTML 1.0!
Copyright © 2007-2019  中国科学院软件研究所 - Feedback
Powered by CSpace