V-cycle Convergence with Unsymmetric Smoothers and Application to an Anisotropic Model Problem

Authors:
Nicolas Neuss
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
1998

Citing 0
Cited 2

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Abstract

We generalize the abstract V-cycle convergence proof of [J. Xu, SIAM Rev., 34 (1992), pp. 581--613] and [H. Yserentant, Acta Numerica, (1993), pp. 285--326] to include unsymmetric smoothing operations as well. Applying our theory to an anisotropic model problem, we obtain optimal results, i.e., robust convergence even when using only one smoothing step of a line-Jacobi, a line Gauss--Seidel, or ILU smoothing.