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Uzawa-Type and Augmented Lagrangian Methods for Double Saddle Point Systems

  • Michele BenziEmail author
  • Fatemeh Panjeh Ali Beik
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 30)

Abstract

We study different types of stationary iterative methods for solving a class of large, sparse linear systems with double saddle point structure. In particular, we propose a class of Uzawa-like methods including a generalized (block) Gauss-Seidel (GGS) scheme and a generalized (block) successive overrelaxation (GSOR) method. Both schemes rely on a relaxation parameter, and we establish convergence intervals for these parameters. Additionally, we investigate the performance of these methods in combination with an augmented Lagrangian approach. Numerical experiments are reported for test problems from two different applications, a mixed-hybrid discretization of the potential fluid flow problem and finite element modeling of liquid crystal directors. Our results show that fast convergence can be achieved with a suitable choice of parameters.

Keywords

Uzawa-like methods Double saddle point problems Augmented Lagrangian method Finite elements Potential fluid flow Liquid crystals 

AMS Subject Classifications:

65F10 65F08 65F50 

Notes

Acknowledgements

We would like to thank Alison Ramage and Miroslav T Open image in new window ma for providing the test problems used in the numerical experiments. We also express our sincere thank to two anonymous referees for their valuable comments and helpful suggestions. The second author is grateful for the hospitality of the Department of Mathematics and Computer Science at Emory University, where part of this work was completed.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Classe di ScienzeScuola Normale SuperiorePisaItaly
  3. 3.Department of MathematicsVali-e-Asr University of RafsanjanRafsanjanIran

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