Novel Approach for solving the discrete Stokes problems based on Augmented Lagrangian and Global Techniques: Application to Saddle-Point Linear Systems from Incompressible flow

• Main Authors: Badahmane, A, Ratnani, A, Sadok, H
• Format: Journal Article
• Language: English
• Published: 04-09-2024
• Subjects: Computer Science - Numerical Analysis; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.2409.02652

In this paper, a novel augmented Lagrangian preconditioner based on global
Arnoldi for accelerating the convergence of Krylov subspace methods applied to
linear systems of equations with a block three-by-three structure, these
systems typically arise from discretizing the Stokes equations using
mixed-finite element methods. In practice, the components of velocity are
always approximated using a single finite element space. More precisely, in two
dimensions, our new approach based on standard space of scalar finite element
basis functions to discretize the velocity space. This componentwise splitting
can be shown to induce a natural block three-by-three structure. Spectral
analyses is 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 computational time.