A new relaxed HSS preconditioner for saddle point problems
This work provides an incremental improvement for solving saddle point problems, which are common in computational fluid dynamics and optimization.
The authors propose a new relaxed HSS preconditioner for saddle point problems, demonstrating its effectiveness through numerical experiments on Stokes problem discretizations.
We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues distribution of the preconditioned matrix are presented. The preconditioned system is solved by a Krylov subspace method like restarted GMRES. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioner.