Preconditioning techniques for the coupled Stokes–Darcy problem: spectral and field-of-values analysis
Fatemeh Panjeh Ali Beik, Michele Benzi
Abstract
Abstract 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.
Topics & Concepts
MathematicsGeneralized minimal residual methodAugmented Lagrangian methodFinite element methodApplied mathematicsBlock (permutation group theory)Linear systemDarcy's lawStokes flowConstraint (computer-aided design)Numerical analysisMathematical optimizationFlow (mathematics)Mathematical analysisGeometryPorous mediumEngineeringThermodynamicsGeotechnical engineeringPhysicsPorosityAdvanced Numerical Methods in Computational MathematicsMatrix Theory and AlgorithmsNumerical methods for differential equations