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Title:
New schemes with fractal error compensation for PDE eigenvalue computations
Author: Sun JiaChang
Keyword: PDE eigenvalues computation ; generalized matrix eigen-problem ; discrete Rayleigh quotient
Source: SCIENCE CHINA-MATHEMATICS
Issued Date: 2014
Volume: 57, Issue:2, Pages:221-244
Indexed Type: SCI
Department: Chinese Acad Sci, Sci Computat Lab, Inst Software, Beijing 100080, Peoples R China.
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.
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.
Language: 英语
WOS ID: WOS:000329791900001
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16701
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Sun JiaChang. New schemes with fractal error compensation for PDE eigenvalue computations[J]. SCIENCE CHINA-MATHEMATICS,2014-01-01,57(2):221-244.
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