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Local Fourier analysis of multigrid smoothers for the Stokes problem
Author(s) -
Bolten Matthias,
Claus Lisa
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900394
Subject(s) - multigrid method , discretization , convergence (economics) , fourier transform , fourier analysis , contrast (vision) , mathematics , finite difference , finite difference method , mathematical analysis , mathematical optimization , partial differential equation , computer science , artificial intelligence , economics , economic growth
We present a local Fourier analysis of the Stokes equations for a finite difference discretization on staggered grids. We compare the commonly used Vanka smoother with a non‐overlapping variant of the Vanka smoother. While the latter is computationally cheaper, the convergence depends severely on the order in which the unknowns are updated. In contrast, the convergence of the overlapping method is not affected by the order.