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An efficient iterative method for the generalized Stokes problem
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DOI：10.1137/S106482759630365X.png)
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The generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow, gives rise to symmetric linear systems of equations. These systems are indefinite due to a set of linear constraints on the velocity, causing difficulty for most preconditioners and iterative methods. This paper presents a novel method to obtain a preconditioned linear system from the original one which is then solved by an iterative method. This new method generates a basis for the velocity space and solves a reduced system which is symmetric and positive definite. Numerical experiments indicating superior convergence compared to existing methods are presented. A natural extension of this method to elliptic problems is also proposed, along with theoretical bounds on the rate of convergence, and results of experiments demonstrating robust and effective preconditioning.
Keyword:
Stokes problem
saddle point
iterative methods
preconditioning
mixed finite elements
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IF:
2.6
论文数:
5.1K
被引数:
1.8W
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