Multi-neighboring grids schemes for solving PDE eigen-problems
文献类型：期刊论文
| 作者 | Sun JiaChang |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2013 |
| 卷号 | 56期号:12页码:2677-2700 |
| 关键词 | PDE eigen-problem discrete Rayleigh quotient multi-neighboring grids schemes B-splines |
| ISSN号 | 1674-7283 |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000328279100015 |
| 公开日期 | 2014-12-16 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/16897]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 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. |
入库方式： OAI收割
来源：软件研究所
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