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| New schemes with fractal error compensation for PDE eigenvalue computations | |
| Sun JiaChang | |
| 2014 | |
| Source | SCIENCE CHINA-MATHEMATICS
 |
| ISSN | 1674-7283 |
| Volume | 57Issue:2Pages:221-244 |
| English Abstract | With an error compensation term in the fractal Rayleigh quotient of PDE eigen-problems, we propose a new scheme by perturbing the mass matrix M (h) to , where K (h) is the corresponding stiff matrix of a 2m - 1 degree conforming finite element with mesh size h for a 2m-order self-adjoint PDE, and the constant C exists in the priority error estimation lambda (j) (h) - lambda (j) similar to Ch (2m) lambda (j) (2) . In particular, for Laplace eigenproblems over regular domains in uniform mesh, e.g., cube, equilateral triangle and regular hexagon, etc., we find the constant and show that in this case the computation accuracy can raise two orders, i.e., from lambda (j) (h) - lambda (j) = O(h (2)) to O(h (4)). Some numerical tests in 2-D and 3-D are given to verify the above arguments.; With an error compensation term in the fractal Rayleigh quotient of PDE eigen-problems, we propose a new scheme by perturbing the mass matrix M (h) to , where K (h) is the corresponding stiff matrix of a 2m - 1 degree conforming finite element with mesh size h for a 2m-order self-adjoint PDE, and the constant C exists in the priority error estimation lambda (j) (h) - lambda (j) similar to Ch (2m) lambda (j) (2) . In particular, for Laplace eigenproblems over regular domains in uniform mesh, e.g., cube, equilateral triangle and regular hexagon, etc., we find the constant and show that in this case the computation accuracy can raise two orders, i.e., from lambda (j) (h) - lambda (j) = O(h (2)) to O(h (4)). Some numerical tests in 2-D and 3-D are given to verify the above arguments. |
| Indexed Type | SCI |
| Keyword | Pde Eigenvalues Computation Generalized Matrix Eigen-problem Discrete Rayleigh Quotient |
| Department | Chinese Acad Sci, Sci Computat Lab, Inst Software, Beijing 100080, Peoples R China. |
| Language | 英语 |
| WOS ID | WOS:000329791900001 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16701 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Sun JiaChang. New schemes with fractal error compensation for PDE eigenvalue computations[J]. SCIENCE CHINA-MATHEMATICS,2014,57(2):221-244. |
| APA | Sun JiaChang.(2014).New schemes with fractal error compensation for PDE eigenvalue computations.SCIENCE CHINA-MATHEMATICS,57(2),221-244. |
| MLA | Sun JiaChang."New schemes with fractal error compensation for PDE eigenvalue computations".SCIENCE CHINA-MATHEMATICS 57.2(2014):221-244. |
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