Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

doi:10.1007/s42967-025-00488-0

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (3): 1076-1094.doi: 10.1007/s42967-025-00488-0

Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

A. Badahmane¹, A. Ratnani¹, H. Sadok²

1. The UM6P Vanguard Center, Mohammed VI Polytechnic University, Benguerir, 43150, Morocco;
2. LMPA, Université du Littoral Côte d'Opale, 62228, Calais Cedex, France

收稿日期:2024-10-12 修回日期:2025-02-13 出版日期:2026-06-20 发布日期:2026-05-29
通讯作者: A. Badahmane, Email: badahmane.achraf@gmail.com E-mail:badahmane.achraf@gmail.com

Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

A. Badahmane¹, A. Ratnani¹, H. Sadok²

1. The UM6P Vanguard Center, Mohammed VI Polytechnic University, Benguerir, 43150, Morocco;
2. LMPA, Université du Littoral Côte d'Opale, 62228, Calais Cedex, France

Received:2024-10-12 Revised:2025-02-13 Online:2026-06-20 Published:2026-05-29
Contact: A. Badahmane, Email: badahmane.achraf@gmail.com E-mail:badahmane.achraf@gmail.com

摘要/Abstract

摘要： In this paper, a novel augmented Lagrangian preconditioner based on the global Arnoldi for accelerating the convergence of Krylov subspace methods is applied to linear systems of equations with a block three-by-three structure, and these systems typically arise from discretizing the Stokes equations using mixed finite-element methods. Spectral analyses are established for the exact versions of these preconditioners. Finally, the obtained numerical results claim that our novel approach is more efficient and robust for solving the discrete Stokes problems. The efficiency of our new approach is evaluated by measuring the computational time.

关键词: Stokes equation, Saddle point problem, Krylov subspace method, Global Krylov subspace method, Augmented Lagrangian-based preconditioning

Abstract: In this paper, a novel augmented Lagrangian preconditioner based on the global Arnoldi for accelerating the convergence of Krylov subspace methods is applied to linear systems of equations with a block three-by-three structure, and these systems typically arise from discretizing the Stokes equations using mixed finite-element methods. Spectral analyses are established for the exact versions of these preconditioners. Finally, the obtained numerical results claim that our novel approach is more efficient and robust for solving the discrete Stokes problems. The efficiency of our new approach is evaluated by measuring the computational time.

Key words: Stokes equation, Saddle point problem, Krylov subspace method, Global Krylov subspace method, Augmented Lagrangian-based preconditioning

中图分类号:

65F10
65F08

A. Badahmane, A. Ratnani, H. Sadok. Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 1076-1094.

参考文献

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Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

Novel Approach for Solving the Discrete Stokes Problems Based on Augmented Lagrangian and Global Techniques with Applications for Stokes Problems

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