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New local generalized shift-splitting preconditioners for saddle point problems

Author

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  • Ling, Si-Tao
  • Liu, Qing-Bing

Abstract

Based on a local generalized shift-splitting of the saddle point matrix with symmetric positive definite (1, 1)-block and symmetric positive semidefinite (2, 2)-block, a new local generalized shift-splitting preconditioner with two shift parameters for solving saddle point problems is proposed. The preconditioner is extracted from a new local generalized shift-splitting iteration and can lead to the unconditional convergence of the iteration. In addition, we consider solving the saddle point systems by preconditioned Krylov subspace methods and discuss some properties of the preconditioned saddle point matrix with a deteriorated preconditioner, such as eigenvalues, eigenvectors, and degree of the minimal polynomial. Numerical experiments arising from a finite element discretization model of the Stokes problem are given to validate the effectiveness of the proposed preconditioner.

Suggested Citation

  • Ling, Si-Tao & Liu, Qing-Bing, 2017. "New local generalized shift-splitting preconditioners for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 58-67.
    • Handle: RePEc:eee:apmaco:v:302:y:2017:i:c:p:58-67
    DOI: 10.1016/j.amc.2017.01.014
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    References listed on IDEAS

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    1. Chen, Cai-Rong & Ma, Chang-Feng, 2015. "A generalized shift-splitting preconditioner for singular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 947-955.
    2. Chen, Fang, 2015. "On choices of iteration parameter in HSS method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 832-837.
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    Cited by:

    1. Shen, Hai-Long & Wu, Hong-Yu & Shao, Xin-Hui, 2021. "A simplified PSS preconditioner for non-Hermitian generalized saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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