Published

Multigrid Methods for the Stokes equations using Distributive Gauss-Seidel Relaxations based on the Least Squares Commutator

Ming Wang and Long Chen

Journal of Scientific Computing, 56(2): 409-431, 2013.

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ABSTRACT:

 A distributive Gauss-Seidel relaxation based on the least
squares commutator is devised for the saddle-point systems arising
from the discretized Stokes equations. Based on that, an efficient
multigrid method is developed for finite element discretizations of
the Stokes equations on both structured grids and unstructured
grids. On rectangular grids, an auxiliary space multigrid method using
one multigrid cycle for the Marker and Cell scheme as auxiliary space
correction and least squares commutator distributive Gauss-Seidel
relaxation as a smoother is shown to be very efficient and outperforms
the popular block preconditioned Krylov subspace methods.