Robust preconditioners for the high-contrast Stokes equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:259

Article

Aksoylu, Burak^1,2  Unlu, Zuhal² 

[1] TOBB Univ Econ & Technol, Dept Math, TR-06560 Ankara, Turkey

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

关键词: Stokes equation;    High-contrast;    High-contrast viscosity;    Robust preconditioning;    Schur complement;    Singular perturbation analysis;   

DOI  :  10.1016/j.cam.2013.10.016

来源: Elsevier

【 摘 要 】

We consider the Stokes equation with high-contrast viscosity coefficients. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by Aksoylu et al. (2008). We examine the performance of our preconditioner against multigrid and provide a comparative study reflecting the effect of the underlying discretization and the aspect ratio of the mesh. We address the rigorous justification of the solver methods, p-Uzawa and p-Minres, used in Aksoylu and Unlu (2013), and compare the results with additional solver method, Schur complement reduction (SCR). We observe that our preconditioner is only contrast size robust under the p-SCR solver. The inexact p-Uzawa solver remains to be the best choice for the most effective performance of our preconditioner as we observe contrast size and mesh size robustness simultaneously in this case. As the contrast size grows asymptotically, we prove and numerically demonstrate that the inexact p-Uzawa solver converges to the exact one. Finally, we show that our preconditioner is contrast size and mesh size robust under p-Minres when the Schur complement solve is accurate enough. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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