A Simplified Non-Equilibrium Splitting Preconditioner for Three-by-Three Block Saddle Point Problems

In this paper, the simplified non-equilibrium splitting preconditioner is established to solve three-by-three block saddle point problems. It is proved that the iteration method produced by preconditioner is conditionally convergent. The spectral properties of the preconditioned matrix are also studied, which shows that the eigenvalues of preconditioned matrix have excellent clustering properties. Numerical results are provided to support the validity of the theoretical results and demonstrate the effectiveness of the studied preconditioner.