A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
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 pro...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/812914 |
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| _version_ | 1832545567731875840 |
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| author | Yidu Yang Wei Jiang Yu Zhang Wenjun Wang Hai Bi |
| author_facet | Yidu Yang Wei Jiang Yu Zhang Wenjun Wang Hai Bi |
| author_sort | Yidu Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3f6dbb6db2374013b83bb2840ac63409 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3f6dbb6db2374013b83bb2840ac634092025-02-03T07:25:21ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/812914812914A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue ProblemsYidu Yang0Wei Jiang1Yu Zhang2Wenjun Wang3Hai Bi4School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaSchool of Physics and Mechanical & Electrical Engineering, Xiamen University, Xiamen 361005, ChinaSchool of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaSchool of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaSchool of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaThis 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.http://dx.doi.org/10.1155/2012/812914 |
| spellingShingle | Yidu Yang Wei Jiang Yu Zhang Wenjun Wang Hai Bi A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems Abstract and Applied Analysis |
| title | A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems |
| title_full | A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems |
| title_fullStr | A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems |
| title_full_unstemmed | A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems |
| title_short | A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems |
| title_sort | two scale discretization scheme for mixed variational formulation of eigenvalue problems |
| url | http://dx.doi.org/10.1155/2012/812914 |
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