On the generalized shift-splitting preconditioner for saddle point problems
This work provides an incremental improvement in preconditioning techniques for saddle point problems, which are common in computational fluid dynamics and optimization.
The paper proposes a generalized shift-splitting preconditioner for saddle point problems with symmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block, derived from an unconditionally convergent stationary iterative method. Numerical experiments on Stokes problem discretizations demonstrate the effectiveness of the preconditioner.
In this paper, the generalized shift-splitting preconditioner is implemented for saddle point problems with symmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. The proposed preconditioner is extracted form a stationary iterative method which is unconditionally convergent. Moreover, a relaxed version of the proposed preconditioner is presented and some properties of the eigenvalues distribution of the corresponding preconditioned matrix are studied. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioners.