Preconditioned Krylov subspace and GMRHSS iteration methods for solving the nonsymmetric saddle point problems. (English) Zbl 1452.65055
Summary: In the present paper, we propose a separate approach as a new strategy to solve the saddle point problem arising from the stochastic Galerkin finite element discretization of Stokes problems. The preconditioner is obtained by replacing the (1,1) and (1,2) blocks in the RHSS preconditioner by others well chosen and the parameter \(\alpha\) in \((2,2)\)-block of the RHSS preconditioner by another parameter \(\beta\). The proposed preconditioner can be used as a preconditioner corresponding to the stationary itearative method or to accelerate the convergence of the generalized minimal residual method (GMRES). The convergence properties of the GMRHSS iteration method are derived. Meanwhile, we analyzed the eigenvalue distribution and the eigenvectors of the preconditioned matrix. Finally, numerical results show the effectiveness of the proposed preconditioner as compared with other preconditioners.
MSC:
| 65F10 | Iterative numerical methods for linear systems |
| 65F08 | Preconditioners for iterative methods |
| 65F50 | Computational methods for sparse matrices |
| 65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
Keywords:
Krylov subspace method; preconditioning; saddle point problem; generalized minimal residual methodSoftware:
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