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A simple and efficient segregated smoother for the discrete Stokes equations

par Gaspar, Francisco J.;Notay, Yvan ;Oosterlee, Cornelis W.;Rodrigo, Carmen
Référence SIAM journal on scientific computing, 36, page (A1187-A1206)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

We consider the multigrid solution of the generalized Stokes equations with a segregated (i.e., equationwise) Gauss-Seidel smoother based on a Uzawa-type iteration. We analyze the smoother in the framework of local Fourier analysis, and obtain an analytic bound on the smoothing factor showing uniform performance for a family of Stokes problems. These results are confirmed by the numerical computation of the two-grid convergence factor for different types of grids and discretizations. Numerical results also show that the actual convergence of the W-cycle is approximately the same as that obtained by a Vanka smoother, despite this latter smoother being significantly more costly per iteration step.