A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems

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Volume 5, Issue 2

Jianlei Li, Zhijiang Zhang and Liang Li

J. Info. Comput. Sci. , 5 (2010), pp. 153-160.

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Abstract

The eigenvalue analysis of the SIMPLE preconditioner for solving two-by-two block linear equations with the (1, 2)-block being the transpose of the (2, 1)-block and the (2, 2)-block being zero was investigated in Li and Vuik [Numer Lin. Alg. Appl., 2004, 11:511-523]. In this note, we extend their ideas by allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and investigate the relationship of the two different formulations spectrum of the SIMPLE preconditioned matrix by using the theory of matrix eigenvalue. And also the SIMPLE type methods are given.

Keywords

SIMPLE preconditioner, eigenvalue analysis, generalized eigenvalue problem, diagonal scaling.

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@Article{JICS-5-153, author = {Jianlei Li, Zhijiang Zhang and Liang Li}, title = {A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems}, journal = {Journal of Information and Computing Science}, year = {2010}, volume = {5}, number = {2}, pages = {153--160}, abstract = { The eigenvalue analysis of the SIMPLE preconditioner for solving two-by-two block linear equations with the (1, 2)-block being the transpose of the (2, 1)-block and the (2, 2)-block being zero was investigated in Li and Vuik [Numer Lin. Alg. Appl., 2004, 11:511-523]. In this note, we extend their ideas by allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and investigate the relationship of the two different formulations spectrum of the SIMPLE preconditioned matrix by using the theory of matrix eigenvalue. And also the SIMPLE type methods are given. }, issn = {3080-180X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22723.html} }

TY - JOUR T1 - A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems AU - Jianlei Li, Zhijiang Zhang and Liang Li JO - Journal of Information and Computing Science VL - 2 SP - 153 EP - 160 PY - 2010 DA - 2010/06 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22723.html KW - SIMPLE preconditioner, eigenvalue analysis, generalized eigenvalue problem, diagonal scaling. AB - The eigenvalue analysis of the SIMPLE preconditioner for solving two-by-two block linear equations with the (1, 2)-block being the transpose of the (2, 1)-block and the (2, 2)-block being zero was investigated in Li and Vuik [Numer Lin. Alg. Appl., 2004, 11:511-523]. In this note, we extend their ideas by allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and investigate the relationship of the two different formulations spectrum of the SIMPLE preconditioned matrix by using the theory of matrix eigenvalue. And also the SIMPLE type methods are given.

Jianlei Li, Zhijiang Zhang and Liang Li. (2010). A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems. Journal of Information and Computing Science. 5 (2). 153-160. doi:

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