An alternating preconditioner for saddle point problems

作者：Peng, Xiao Fei; Li, Wen^*

来源：Journal of Computational and Applied Mathematics, 2010, 234(12): 3411-3423.

DOI：10.1016/j.cam.2010.05.003

• Saddle point problems
• Matrix splitting
• The alternating preconditioner
• Eigenvalue distribution
• Convergence rate

Based on matrix splittings, a new alternating preconditioner with two parameters is proposed for solving saddle point problems. Some theoretical analyses for the eigenvalues of the associated preconditioned matrix are given. The choice of the parameters is considered and the quasi-optimal parameters are obtained. The new preconditioner with these quasi-optimal parameters significantly improves the convergence rate of the generalized minimal residual (GMRES) iteration. Numerical experiments from the linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially on the larger viscosity parameter nu. Further extensions of the preconditioner to generalized saddle point matrices are also checked.

• 出版日期2010-10-15
• 单位中南大学; 华南师范大学