A variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems

作者：Zhang, Juli; Gu, Chuanqing^*

来源：BIT Numerical Mathematics, 2016, 56(2): 587-604.

DOI：10.1007/s10543-015-0590-9

• Saddle point problems
• Preconditioning
• Spectral properties
• Krylov subspace method
• Navier-Stokes equation

For nonsymmetric saddle point problems, Pan et al. (Appl Math Comput 172:762-771, 2006) proposed a deteriorated positive-definite and skew-Hermitian splitting (DPSS) preconditioner. In this paper, a variant of the DPSS preconditioner is proposed to accelerate the convergence of the associated Krylov subspace methods. The new preconditioner is much closer to the coefficient matrix than the DPSS preconditioner. The spectral properties of the new preconditioned matrix are analyzed. Theorem which provides the dimension of the Krylov space for the preconditioned matrix is obtained. Numerical experiments of a model Navier-Stokes problem are presented to illustrate the effectiveness of the new preconditioner.

• 出版日期2016-6
• 单位上海大学; 浙江农林大学