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Title: Robust preconditioners for the high-contrast Stokes equation
Authors: Aksoylu, Burak
Keywords: Stokes equation
 High-contrast viscosity
 Robust preconditioning
 Schur complement
 Singular perturbation analysis
Issue Date: Mar-2014
Publisher: Elsevier Science Bv
Source: Aksoylu, B., & Unlu, Z. (2014). Robust preconditioners for the high-contrast Stokes equation. Journal of Computational and Applied Mathematics, 259, 944-954.
Abstract: 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.
ISSN: 0377-0427
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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