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| Multi-neighboring grids schemes for solving PDE eigen-problems | |
| Sun JiaChang | |
| 2013 | |
| Source | SCIENCE CHINA-MATHEMATICS
 |
| ISSN | 1674-7283 |
| Volume | 56Issue:12Pages:2677-2700 |
| 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.; 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. |
| Indexed Type | SCI |
| Keyword | Pde Eigen-problem Discrete Rayleigh Quotient Multi-neighboring Grids Schemes B-splines |
| Department | Chinese Acad Sci, Inst Software, Sci Computat Lab, Beijing 100080, Peoples R China. |
| Language | 英语 |
| WOS ID | WOS:000328279100015 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16897 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
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