A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow
We consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not be zero. The eigenvalue analysis of the SIMPLE preconditi...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/564132 |
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| author | Shi-Liang Wu Feng Chen Xiao-Qi Niu |
| author_facet | Shi-Liang Wu Feng Chen Xiao-Qi Niu |
| author_sort | Shi-Liang Wu |
| collection | DOAJ |
| description | We consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where
the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not
be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented.
The relationship between the two different formulations spectrum of the SIMPLE preconditioned matrix is established by using the theory of matrix eigenvalue, and some corresponding results in recent article by Li and Vuik (2004) are extended. |
| format | Article |
| id | doaj-art-d01c2eb1395b4215893a5c3d25bfb5f2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d01c2eb1395b4215893a5c3d25bfb5f22025-02-03T05:54:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/564132564132A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible FlowShi-Liang Wu0Feng Chen1Xiao-Qi Niu2School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaWe consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented. The relationship between the two different formulations spectrum of the SIMPLE preconditioned matrix is established by using the theory of matrix eigenvalue, and some corresponding results in recent article by Li and Vuik (2004) are extended.http://dx.doi.org/10.1155/2012/564132 |
| spellingShingle | Shi-Liang Wu Feng Chen Xiao-Qi Niu A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow Journal of Applied Mathematics |
| title | A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow |
| title_full | A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow |
| title_fullStr | A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow |
| title_full_unstemmed | A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow |
| title_short | A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow |
| title_sort | note on the eigenvalue analysis of the simple preconditioning for incompressible flow |
| url | http://dx.doi.org/10.1155/2012/564132 |
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