On the analysis of block smoothers for saddle point problems

Daniel Drzisga; Lorenz John; Ulrich Rüde; Barbara Wohlmuth; Walter Zulehner

doi:10.1137/16M1106304

On the analysis of block smoothers for saddle point problems

Daniel Drzisga, Lorenz John, Ulrich Rüde, Barbara Wohlmuth, Walter Zulehner

Chair of Numerical Analysis

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes for saddle point problems. A unified framework to analyze the smoothing properties is presented. The introduction of a new symmetric variant allows us to obtain estimates for popular lower and upper block triangular variants. Numerical experiments for a low order stable and a stabilized P1-conforming discretization for the Stokes problem illustrate the theory. Finally, large-scale three-dimensional examples demonstrate the potential of this class of smoothers.

Original language	English
Pages (from-to)	932-960
Number of pages	29
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/16M1106304
State	Published - 2018

Keywords

Multigrid
Saddle point problem
Smoothing property
Stokes problem
Uzawa method

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10.1137/16M1106304

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abstract = "We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes for saddle point problems. A unified framework to analyze the smoothing properties is presented. The introduction of a new symmetric variant allows us to obtain estimates for popular lower and upper block triangular variants. Numerical experiments for a low order stable and a stabilized P1-conforming discretization for the Stokes problem illustrate the theory. Finally, large-scale three-dimensional examples demonstrate the potential of this class of smoothers.",

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AU - John, Lorenz

AU - Rüde, Ulrich

AU - Wohlmuth, Barbara

AU - Zulehner, Walter

PY - 2018

Y1 - 2018

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AB - We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes for saddle point problems. A unified framework to analyze the smoothing properties is presented. The introduction of a new symmetric variant allows us to obtain estimates for popular lower and upper block triangular variants. Numerical experiments for a low order stable and a stabilized P1-conforming discretization for the Stokes problem illustrate the theory. Finally, large-scale three-dimensional examples demonstrate the potential of this class of smoothers.

KW - Multigrid

KW - Saddle point problem

KW - Smoothing property

KW - Stokes problem

KW - Uzawa method

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On the analysis of block smoothers for saddle point problems

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Keywords

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