Topics in matrix analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
Iterative methods for solving linear systems
Iterative methods for solving linear systems
A Deflated Version of the Conjugate Gradient Algorithm
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Analysis of a Stokes interface problem
Numerische Mathematik
An Iterative Method for the Stokes-Type Problem with Variable Viscosity
SIAM Journal on Scientific Computing
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem
Applied Numerical Mathematics
Computational Optimization and Applications
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Many mathematical models involve flow equations characterized by nonconstant viscosity, and a Stokes-type problem with variable viscosity coefficient arises. Appropriate block diagonal preconditioners for the resulting algebraic saddle point linear system produce well-clustered spectra, except for a few interior isolated eigenvalues which may tend to approach zero. These outliers affect the convergence of Krylov subspace system solvers, causing a possibly long stagnation phase. In this paper we characterize the influence of the spectral properties of the preconditioner on the final spectrum of the saddle point matrix by providing accurate spectral intervals depending on the involved operators. Moreover, we suggest that the stagnation phase may be completely eliminated by means of an augmentation procedure, where approximate spectral eigenspace information can be injected. We show that the modifications to the original code are minimal and can be easily implemented. Numerical experiments confirm our findings.