Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems

Daniel Jodlbauer; Ulrich Langer; Thomas Wick; Walter Zulehner

doi:10.48550/arXiv.2205.15770

Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems

Daniel Jodlbauer, Ulrich Langer, Thomas Wick, Walter Zulehner

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

Abstract

We consider the widely used continuous \scrQ_k-\scrQ_k-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.

Original language	English
Pages (from-to)	A1599-A1627
Journal	SIAM Journal on Scientific Computing
Volume	46
Issue number	3
E-pub ahead of print	9 May 2024
DOIs	https://doi.org/10.48550/arXiv.2205.15770 https://doi.org/10.1137/22M1504184
Publication status	Published - 2024

Keywords

matrix-free implementation
mixed finite element discretization
multigrid methods
Stokes and generalized Stokes problems

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.48550/arXiv.2205.15770Licence: CC BY 4.0
10.1137/22M1504184

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title = "Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems",

abstract = "We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Sch{\"o}berl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.",

keywords = "matrix-free implementation, mixed finite element discretization, multigrid methods, Stokes and generalized Stokes problems",

author = "Daniel Jodlbauer and Ulrich Langer and Thomas Wick and Walter Zulehner",

note = "Publisher Copyright: Copyright {\textcopyright} by SIAM.",

year = "2024",

doi = "10.48550/arXiv.2205.15770",

language = "English",

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AU - Jodlbauer, Daniel

AU - Langer, Ulrich

AU - Wick, Thomas

AU - Zulehner, Walter

PY - 2024

Y1 - 2024

N2 - We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.

AB - We consider the widely used continuous \scrQk-\scrQk-1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions. For the fast solution of the corresponding symmetric, but indefinite system of finite element equations, we propose and analyze matrix-free monolithic geometric multigrid solvers that are based on appropriately scaled Chebyshev-Jacobi smoothers. The analysis is based on results by Schöberl and Zulehner (2003). We present and discuss several numerical results for typical benchmark problems.

KW - matrix-free implementation

KW - mixed finite element discretization

KW - multigrid methods

KW - Stokes and generalized Stokes problems

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DO - 10.48550/arXiv.2205.15770

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SP - A1599-A1627

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

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ER -

Matrix-Free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems

Abstract

Keywords

ASJC Scopus subject areas

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