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A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Joint Authors
Wang, Wenjun
Bi, Hai
Yang, Yidu
Jiang, Wei
Zhang, Yu
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-29, 29 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-15
Country of Publication
Egypt
No. of Pages
29
Main Subjects
Abstract EN
This paper discusses highly efficient discretization schemes for mixed variational formulation of eigenvalue problems.
A new finite element two-scale discretization scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems.
With this scheme, the solution of an eigenvalue problem on a fine grid Kh is reduced to the solution of an eigenvalue problem on a much coarser grid KH and the solution of a linear algebraic system on the fine grid Kh.
Theoretical analysis shows that the scheme has high efficiency.
For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by taking H=O(h4), and when using the Pk+1-Pk element to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by taking H=O(h3).
Finally, numerical experiments are presented to support the theoretical analysis.
American Psychological Association (APA)
Yang, Yidu& Jiang, Wei& Zhang, Yu& Wang, Wenjun& Bi, Hai. 2012. A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-29.
https://search.emarefa.net/detail/BIM-500063
Modern Language Association (MLA)
Yang, Yidu…[et al.]. A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems. Abstract and Applied Analysis No. 2012 (2012), pp.1-29.
https://search.emarefa.net/detail/BIM-500063
American Medical Association (AMA)
Yang, Yidu& Jiang, Wei& Zhang, Yu& Wang, Wenjun& Bi, Hai. A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-29.
https://search.emarefa.net/detail/BIM-500063
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-500063