Shift-splitting preconditioners for saddle point problems

• Autores: Yang Cao, Jun Du, Qiang Niu
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 272, Nº 1, 2014, págs. 239-250
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.05.017
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• Resumen

  • In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners.