Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows

Xin He; Cornelis Vuik

doi:10.1016/j.jcp.2020.109286

Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows

Xin He, Cornelis Vuik^*

^*Corresponding author for this work

Numerical Analysis

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

3 Citations (Scopus)

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Abstract

This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context determines the most efficient Schur complement approximation and investigates the effect of the Reynolds number, mesh anisotropy and refinement on the optimal choice. Furthermore, the advantage over the traditional Schur complement approximation is exhibited.

Original language	English
Article number	109286
Number of pages	18
Journal	Journal of Computational Physics
Volume	408
DOIs	https://doi.org/10.1016/j.jcp.2020.109286
Publication status	Published - 1 May 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Augmented Lagrangian preconditioner
Block structured preconditioners
Navier-Stokes equations
Schur complement approximations
Stabilized finite element method

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10.1016/j.jcp.2020.109286

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abstract = "This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context determines the most efficient Schur complement approximation and investigates the effect of the Reynolds number, mesh anisotropy and refinement on the optimal choice. Furthermore, the advantage over the traditional Schur complement approximation is exhibited.",

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AB - This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context determines the most efficient Schur complement approximation and investigates the effect of the Reynolds number, mesh anisotropy and refinement on the optimal choice. Furthermore, the advantage over the traditional Schur complement approximation is exhibited.

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Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows

Abstract

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Keywords

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