Preconditioning techniques for the coupled Stokes–Darcy problem: spectral and field-of-values analysis

We study the performance of some preconditioning techniques for a class of block three-by-three linear systems of equations arising from finite element discretizations of the coupled Stokes–Darcy flow problem. In particular, we investigate preconditioning techniques including block preconditioners,...

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Bibliographic Details
Published in:Numerische Mathematik 2022-02, Vol.150 (2), p.257-298
Main Authors: Beik, Fatemeh Panjeh Ali, Benzi, Michele
Format: Article
Language:English
Subjects:
Linear systems
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Preconditioning
Simulation
Theoretical
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Summary:We study the performance of some preconditioning techniques for a class of block three-by-three linear systems of equations arising from finite element discretizations of the coupled Stokes–Darcy flow problem. In particular, we investigate preconditioning techniques including block preconditioners, constraint preconditioners, and augmented Lagrangian-based ones. Spectral and field-of-value analyses are established for the exact versions of these preconditioners. The result of numerical experiments are reported to illustrate the performance of inexact variants of the various preconditioners used with flexible GMRES in the solution of a 3D test problem with large jumps in the permeability.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-021-01267-8