Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization

Timo Heister; Gerd Rapin

doi:10.1002/fld.3654

Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization

Timo Heister, Gerd Rapin

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

58 Scopus citations

Abstract

Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.

Original language	English (US)
Pages (from-to)	118-134
Number of pages	17
Journal	International Journal for Numerical Methods in Fluids
Volume	71
Issue number	1
DOIs	https://doi.org/10.1002/fld.3654
State	Published - Jan 29 2012
Externally published	Yes

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10.1002/fld.3654

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title = "Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization",

abstract = "Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. {\textcopyright} 2012 John Wiley & Sons, Ltd.",

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note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The majority of the research was done while both authors worked at the University of Gottingen, Germany. Timo Heister was partially supported by the German Research Foundation (DFG) through the Research Training Group GK 1023. This publication is based, in part, on the work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Heister, Timo

AU - Rapin, Gerd

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N2 - Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.

AB - Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.

UR - http://hdl.handle.net/10754/598100

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Efficient augmented Lagrangian-type preconditioning for the Oseen problem using Grad-Div stabilization

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