New schemes with fractal error compensation for PDE eigenvalue computations

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	New schemes with fractal error compensation for PDE eigenvalue computations
	Sun JiaChang
	2014
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	57 期号:2 页码:221-244
摘要	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.
收录类别	SCI
关键词	Pde Eigenvalues Computation Generalized Matrix Eigen-problem Discrete Rayleigh Quotient
部门归属	Chinese Acad Sci, Sci Computat Lab, Inst Software, Beijing 100080, Peoples R China.
语种	英语
WOS记录号	WOS:000329791900001
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16701
专题	中国科学院软件研究所
推荐引用方式 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.