A new Bramble-Pasciak-like preconditioner forsaddle point problems

Xiao-Fei Peng; Wen Li

doi:10.3934/naco.2012.2.823

Article Contents

2012, Volume 2, Issue 4: 823-838. Doi: 10.3934/naco.2012.2.823

This issue Previous Article A generalization of the positive-definite and skew-Hermitian splitting iteration Next Article Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices

A new Bramble-Pasciak-like preconditioner for saddle point problems

Xiao-Fei Peng^1, and
Wen Li^2,

1.
Nanhai College, South China Normal University, Foshan 528225
2.
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631

Received: December 2011

Revised: October 2012

Published: November 2012

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Abstract

A new Bramble-Pasciak-like preconditioner with parameter is proposed for solving a linear system in the saddle point form. The system can be reformulated as a symmetric positive definite system with respect to some inner product and thus can be solved by the Bramble-Pasciak conjugate gradient (BPCG) method. Based on the spectral condition number of the associated system, the quasi-optimal parameters can be obtained to improve the convergence rate of the BPCG method. Numerical experiments on the Stokes problem are given to illustrate our theoretical results.

Keywords:

Saddle point problems,
Bramble-Pasciak-like preconditioner,
Bramble-Pasciak conjugate gradient method,
spectral condition number,
convergence rate.

Mathematics Subject Classification: Primary: 65F10, 65F15.

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References

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