A conforming auxiliary space preconditioner for the mass conserving stress-yielding method

Lukas Kogler; Philip L. Lederer; Joachim Schöberl

doi:10.1002/nla.2503

A conforming auxiliary space preconditioner for the mass conserving stress-yielding method

Lukas Kogler, Philip L. Lederer^*, Joachim Schöberl

^*Corresponding author for this work

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

3 Citations (Scopus)

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Abstract

We are studying the efficient solution of the system of linear equations stemming from the mass conserving stress-yielding (MCS) discretization of the Stokes equations. We perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on robustness in the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.

Original language	English
Article number	e2503
Number of pages	31
Journal	Numerical linear algebra with applications
Volume	30
Issue number	5
Early online date	7 May 2023
DOIs	https://doi.org/10.1002/nla.2503
Publication status	Published - Oct 2023
Externally published	Yes

Keywords

auxiliary space preconditioner
exact divergence-free velocity
high order robustness
iterative solver
Stokes equations

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10.1002/nla.2503Licence: CC BY

ArticleFinal published version, 1.77 MBLicence: CC BY

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abstract = "We are studying the efficient solution of the system of linear equations stemming from the mass conserving stress-yielding (MCS) discretization of the Stokes equations. We perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on robustness in the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.",

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AB - We are studying the efficient solution of the system of linear equations stemming from the mass conserving stress-yielding (MCS) discretization of the Stokes equations. We perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on robustness in the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.

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KW - exact divergence-free velocity

KW - high order robustness

KW - iterative solver

KW - Stokes equations

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A conforming auxiliary space preconditioner for the mass conserving stress-yielding method

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Keywords

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