A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems

Authors

  • Jianlei Li, Zhijiang Zhang and Liang Li

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.

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Published

2025-08-29

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Section

Articles