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Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows

Giani, Stefano; Houston, Paul

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Authors

Stefano Giani

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths



Abstract

In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. To define the necessary coarse-level solver required for the definition of the proposed preconditioner, we exploit ideas from composite finite element methods, which allow for the definition of finite element schemes on general meshes consisting of polygonal (agglomerated) elements. The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two- and three-dimensions.

Citation

Giani, S., & Houston, P. (2014). Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows. Numerical Mathematics, 7(2), https://doi.org/10.1017/S100489790000091X

Journal Article Type Article
Publication Date May 1, 2014
Deposit Date Aug 26, 2015
Publicly Available Date Mar 29, 2024
Journal Numerical Mathematics: Theory, Methods and Applications
Electronic ISSN 1004-8979
Peer Reviewed Peer Reviewed
Volume 7
Issue 2
DOI https://doi.org/10.1017/S100489790000091X
Public URL https://nottingham-repository.worktribe.com/output/995823
Publisher URL http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9683854&fulltextType=RA&fileId=S100489790000091X
Additional Information First published in Numerical Mathematics: Theory, Methods, Mathematics in volume 7 issue 2, 2014, published by Global Science Press.

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